bluuebunny/crossref_metadata_2025 huggingface dataset:
A phenomenon of reciprocity in the universal Steenrod algebra
Authors: Lomonaco Luciano
Published: June 2012

In this paper we compute the cohomology algebra of certain subalgebras

L
r

{L_r}

and certain quotients

K
s

{K_s}

of the

mod

2

\bmod \, 2

universal Steenrod algebra

Q
Q

, the algebra of cohomology operations for

H
∞

{H_\infty }

-ring spectra (see

[
M
]

[\text {M}]

). We prove that
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper E x t Subscript upper L Sub Subscript r Subscript Baseline left-parenthesis upper F 2 comma upper F 2 right-parenthesis approximately-equals upper K Subscript negative k plus 1 Baseline comma upper E x t Subscript upper K Sub Subscript s Subscript Baseline left-parenthesis upper F 2 comma upper F 2 right-parenthesis approximately-equals upper L Subscript negative s plus 1 Baseline">

Ext

L
r

⁡
(

F
2

,

F
2

)
≅

K

−
k
+
1

,

Ext

K
s

⁡
(

F
2

,

F
2

)
≅

L

−
s
+
1

\operatorname {Ext}_{{L_r}}({F_2},{F_2}) \cong {K_{ - k + 1}}, \qquad \operatorname {Ext}_{{K_s}}({F_2},{F_2}) \cong {L_{ - s + 1}}

\]
with

r
r

,

s
s

integers and

r
≤
1

r \leq 1

,

s
≥
0

s \geq 0

. We also observe that some of the algebras

L
r

{L_r}

,

K
s

{K_s}

are well known objects in stable homotopy theory and in fact our computation generalizes the fact that

H

∗

(

A
L

)
≅

Λ

opp

{H^{\ast } }({A_L}) \cong \Lambda ^{{\text {opp}}}

and

H

∗

(

Λ

opp

)
≅

A
L

{H^{\ast } }({\Lambda ^{{\text {opp}}}}) \cong {A_L}

(see, for instance,

[
P
]

[\text {P}]

). Here

A
L

{A_L}

is the Steenrod algebra for simplicial restricted Lie algebras and

Λ
\Lambda

is the

E
1

{E_1}

-term of the Adams spectral sequence discovered in

[
B-S
]

[\text {B-S}]

.
Families of sets of positive measure
Authors: Plebanek Grzegorz
Published: June 2012

We present a combinatorial description of those families

P

\mathcal {P}

of sets, for which there is a finite measure

μ
\mu

such that

inf
{
μ
(
P
)
:
P
∈

P

}
>
0

\inf \{ \mu (P):P \in \mathcal {P}\} > 0

. This result yields a topological characterization of measure-compactness and Borel measure-compactness. It is also applied to a problem on the existence of regular measure extensions.
The equivariant Hurewicz map
Authors: Lewis L. Gaunce
Published: June 2012

Let

G
G

be a compact Lie group,

Y
Y

be a based

G
G

-space, and

V
V

be a

G
G

-representation. If

π
V
G

(
Y
)

\pi _V^G(Y)

is the equivariant homotopy group of

Y
Y

in dimension

V
V

and

H
V
G

(
Y
)

H_V^G(Y)

is the equivariant ordinary homology group of

Y
Y

with Burnside ring coefficients in dimension

V
V

, then there is an equivariant Hurewicz map
\[

h
:

π
V
G

(
Y
)
→

H
V
G

(
Y
)
.

h:\pi _V^G(Y) \to H_V^G(Y).

\]
One should not expect this map to be an isomorphism, since

H
V
G

(
Y
)

H_V^G(Y)

must be a module over the Burnside ring, but

π
V
G

(
Y
)

\pi _V^G(Y)

need not be. However, here it is shown that, under the obvious connectivity conditions on

Y
Y

, this map induces an isomorphism between

H
V
G

(
Y
)

H_V^G(Y)

and an algebraically defined modification of

π
V
G

(
Y
)

\pi _V^G(Y)

. The equivariant Freudenthal Suspension Theorem contains a technical hypothesis that has no nonequivariant analog. Our results shed some light on the behavior of the suspension map when this rather undesirable technical hypothesis is not satisfied.
Homological theory of idempotent ideals
Authors: Auslander M. , Platzeck M. I. , Todorov G.
Published: June 2012

Let

Λ
\Lambda

be an artin algebra

A

\mathfrak {A}

and a two-sided ideal of

Λ
\Lambda

. Then

A

\mathfrak {A}

is the trace of a projective

Λ
\Lambda

-module

P
P

in

Λ
\Lambda

. We study how the homological properties of the categories of finitely generated modules over the three rings

Λ

/

A

\Lambda /\mathfrak {A}

,

Λ
\Lambda

and the endomorphism ring of

P
P

are related. We give some applications of the ideas developed in the paper to the study of quasi-hereditary algebras.
Automorphisms of torsion-free nilpotent groups of class two
Authors: Dugas Manfred , Göbel Rüdiger
Published: June 2012

We construct

2
2

-divisible, torsion-free abelian groups

G
G

admitting an alternating bilinear map. We use these groups

G
G

to find nilpotent groups

N
N

of class

2
2

such that

Aut
⁡
(
N
)

\operatorname {Aut}(N)

modulo a natural normal subgroup is a prescribed group.
A local Weyl’s law, the angular distribution and multiplicity of cusp forms on product spaces
Authors: Huntley Jonathan , Tepper David
Published: June 2012

Let

Γ

/

H

\Gamma /\mathcal {H}

be a finite volume symmetric space with

H

\mathcal {H}

the product of half planes. Let

Δ
i

{\Delta _i}

be the Laplacian on the

i
i

th half plane, and assume that we have a cusp form

ϕ
\phi

, so we have

Δ
i

ϕ
=

λ
i

ϕ

{\Delta _i}\phi = {\lambda _i}\phi

for

i
=
1
,
2
,
…
,
n

i = 1,2, \ldots ,n

. Let

λ
→

=
(

λ
1

,
…
,

λ
n

)

\vec \lambda = ({\lambda _1}, \ldots ,{\lambda _n})

and let
\[

R
=

r
1
2

+
⋯
+

r
n
2

R = \sqrt {r_1^2 + \cdots + r_n^2}

\]
with

r
i
2

+

1
4

=

λ
i

r_i^2 + \frac {1} {4} = {\lambda _i}

. Letting

r
→

=
(

r
1

,
…
,

r
n

)

\vec r = ({r_1}, \ldots ,{r_n})

, we let

M
(

r
→

)

M(\vec r)

denote the dimension of the space of cusp forms with eigenvalue

λ
→

\vec \lambda

. More generally, let

M
(

r
→

,
a
)

M(\vec r,a)

denote the number of independent eigenfunctions such that the

r
→

\vec r

associated to an eigenfunction is inside the ball of radius

a
a

, centered at

r
→

\vec r

. We will define a function

f
(

r
→

)

f(\vec r)

, which is generally equal to a linear sum of products of the

r
i

{r_i}

. We prove the following theorems. Theorem 1.
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper M left-parenthesis ModifyingAbove r With right-arrow right-parenthesis equals upper O left-parenthesis StartFraction f left-parenthesis ModifyingAbove r With right-arrow right-parenthesis Over left-parenthesis log upper R right-parenthesis Superscript n Baseline EndFraction right-parenthesis period">

M
(

r
→

)
=
O

(

f
(

r
→

)

(
log
⁡
R

)
n

)

.

M(\vec r) = O\left (\frac {f(\vec r)} {(\log R)^n} \right ).

\]
Theorem 2.
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper M left-parenthesis ModifyingAbove r With right-arrow comma upper A right-parenthesis equals 2 Superscript n Baseline f left-parenthesis ModifyingAbove r With right-arrow right-parenthesis plus upper O left-parenthesis StartFraction f left-parenthesis ModifyingAbove r With right-arrow right-parenthesis Over log upper R EndFraction right-parenthesis period">

M
(

r
→

,
A
)
=

2
n

f
(

r
→

)
+
O

(

f
(

r
→

)

log
⁡
R

)

.

M (\vec {r}, A) = 2^n f(\vec {r})+O\left (\frac {f(\vec r)}{\log R} \right ).

\]
The structure of solutions of a semilinear elliptic equation
Authors: Cheng Kuo-Shung , Lin Tai Chia
Published: June 2012

We give a complete classification of solutions of the elliptic equation

Δ
u
+
K
(
x
)

e

2
u

=
0

\Delta u + K(x){e^{2u}} = 0

in

R

n

,
n
≥
3

\mathbb {R}^n, n \geq 3

, for some interesting cases of

K
K

.
Existence of positive nonradial solutions for nonlinear elliptic equations in annular domains
Authors: Lin Song-Sun
Published: June 2012

We study the existence of positive nonradial solutions of equation

Δ
u
+
f
(
u
)
=
0

\Delta u + f(u) = 0

in

Ω
a

{\Omega _a}

,

u
=
0

u = 0

on

∂

Ω
a

\partial {\Omega _a}

, where

Ω
a

=
{
x
∈

R

n

:
a
>

|

x

|

>
1
}

{\Omega _a} = \{ x \in {\mathbb {R}^n}:a > |x| > 1\}

is an annulus in

R

n

{\mathbb {R}^n}

,

n
≥
2

n \geq 2

, and

f
f

is positive and superlinear at both

0
0

and

∞
\infty

. We use a bifurcation method to show that there is a nonradial bifurcation with mode

k
k

at

a
k

∈
(
0
,
1
)

{a_k} \in (0,1)

for any positive integer

k
k

if

f
f

is subcritical and for large

k
k

if

f
f

is supercritical. When

f
f

is subcritical, then a Nehari-type variational method can be used to prove that there exists

a

∗

∈
(
0
,
1
)

{a^{\ast } } \in (0,1)

such that for any

a
∈
(

a

∗

,
1
)

a \in ({a^{\ast } },1)

, the equation has a nonradial solution on

Ω
a

{\Omega _a}

.
Distortion theorems for Bloch functions
Authors: Liu Xiang Yang , Minda David
Published: June 2012

We establish various distortion theorems for both normalized locally schlicht Bloch functions and normalized Bloch function with branch points. These distortion theorems give lower bounds on either

|

f
′
(
z
)

|

|f\prime (z)|

or

Re
⁡
f
′
(
z
)

\operatorname {Re} f\prime (z)

; most of our distortion theorems are sharp and all extremal functions identified. The main tools used in establishing these distortion theorems are the classical form of Julia’s Lemma and a new version of Julia’s Lemma that applies to certain multiple-valued analytic functions. As applications of these distortion theorems, we obtain known lower bounds for various Bloch constants and also establish improved lower bounds on a number of Marden constants for Bloch, normal and Yosida functions.
Global existence, large time behavior and life span of solutions of a semilinear parabolic Cauchy problem
Authors: Lee Tzong-Yow , Ni Wei-Ming
Published: June 2012

We investigate the behavior of the solution

u
(
x
,
t
)

u(x,t)

of
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartLayout Enlarged left-brace 1st Row 1st Column StartFraction partial-differential u Over partial-differential t EndFraction equals normal upper Delta u plus u Superscript p Baseline 2nd Column a m p semicolon in double-struck upper R Superscript n Baseline times left-parenthesis 0 comma upper T right-parenthesis comma 2nd Row 1st Column u left-parenthesis x comma 0 right-parenthesis equals phi left-parenthesis x right-parenthesis 2nd Column a m p semicolon in double-struck upper R Superscript n Baseline comma EndLayout">

{

∂
u

∂
t

=
Δ
u
+

u
p

a
m
p
;

in

R

n

×
(
0
,
T
)
,

u
(
x
,
0
)
=
φ
(
x
)

a
m
p
;

in

R

n

,

\left \{ {\begin {array}{*{20}{c}} {\frac {{\partial u}} {{\partial t}} = \Delta u + {u^p}} \hfill & {{\text {in}}\;{\mathbb {R}^n} \times (0,T),} \hfill \\ {u(x,0) = \varphi (x)} \hfill & {{\text {in}}\;{\mathbb {R}^n},} \hfill \\ \end {array} } \right .

\]
where

Δ
=

∑

i
=
1

n

∂
2

/

∂

x
i

2

\Delta = \sum \nolimits _{i = 1}^n {{\partial ^2}/\partial _{{x_i}}^2}

is the Laplace operator,

p
>
1

p > 1

is a constant,

T
>
0

T > 0

, and

φ
\varphi

is a nonnegative bounded continuous function in

R

n

{\mathbb {R}^n}

. The main results are for the case when the initial value

φ
\varphi

has polynomial decay near

x
=
∞

x = \infty

. Assuming

φ
∼
λ

(
1
+

|

x

|

)

−
a

\varphi \sim \lambda {(1 + |x|)^{ - a}}

with

λ
\lambda

,

a
>
0

a > 0

, various questions of global (in time) existence and nonexistence, large time behavior or life span of the solution

u
(
x
,
t
)

u(x,t)

are answered in terms of simple conditions on

λ
\lambda

,

a
a

,

p
p

and the space dimension

n
n

.
The index of a Brauer class on a Brauer-Severi variety
Authors: Schofield Aidan , Van den Bergh Michel
Published: June 2012

Let

D
D

and

E
E

be central division algebras over

k
k

; let

K
K

be the generic splitting field of

E
E

; we show that the index of

D

⊗
k

K

D{ \otimes _k}K

is the minimum of the indices of

D
⊗

E

⊗
i

D \otimes {E^{ \otimes i}}

as

i
i

varies. We use this to calculate the index of

D
D

under related central extensions and to construct division algebras with special properties.
A Haar-type theory of best 𝐿₁-approximation with constraints
Authors: Kroó András , Schmidt Darrell
Published: June 2012

A general setting for constrained

L
1

{L^1}

-approximation is presented. Let

U
n

{U_n}

be a finite dimensional subspace of

C
[
a
,
b
]

C[a,b]

and

L
L

be a linear operator from

U
n

{U_n}

to

C
r

(
K
)

(
r
=
0
,
1
)

{C^r}(K)\;(r = 0,1)

where

K
K

is a finite union of disjoint, closed, bounded intervals. For

υ
,
u
∈

C
r

(
K
)

\upsilon ,u \in {C^r}(K)

with

υ
>
u

\upsilon > u

, the approximating set is
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="ModifyingAbove upper U With tilde Subscript n Baseline left-parenthesis upsilon comma u right-parenthesis equals StartSet p element-of upper U Subscript n Baseline colon upsilon less-than-or-equal-to upper L p less-than-or-equal-to u on upper K EndSet">

U
~

n

(
υ
,
u
)
=
{
p
∈

U
n

:
υ
≤
L
p
≤
u

on

K
}

{\tilde U_n}(\upsilon ,u) = \{ p \in {U_n}:\upsilon \leq Lp \leq u\;{\text {on}}\;K\}

and the norm is

‖
f

‖
w

=

∫
a
b

|

f

|

w

d
x

\|f\|_w = \int _a^b {|f|w\,dx}

where

w
w

a positive continuous function on

[
a
,
b
]

[a,b]

. We obtain necessary and sufficient conditions for

U
~

n

(
υ
,
u
)

{\tilde U_n}(\upsilon ,u)

to admit unique best

‖

⋅

‖
w

\|\;\cdot \;\|_w

-approximations to all

f
∈
C
[
a
,
b
]

f \in C[a,b]

for all positive continuous

w
w

and all

υ
,
u
∈

C
r

(
K
)

(
r
=
0
,
1
)

\upsilon ,u \in {C^r}(K)\;(r = 0,1)

satisfying a nonempty interior condition. These results are applied to several

L
1

{L^1}

-approximation problems including polynomial and spline approximation with restricted derivatives, lacunary polynomial approximation with restricted derivatives, and others.
The level manifold of a generalized Toda equation hierarchy
Authors: Nakamura Yoshimasa
Published: June 2012

The finite nonperiodic Toda lattice equation induces a linear one-parameter flow on a space of rational functions. The level manifold of the Toda equation hierarchy is shown to be a product of lines. Our main results establish a generalization of this Toda hierarchy which will be called the cyclic-Toda hierarchy. It is proved that the cyclic-Toda hierarchy is completely integrable and its level manifold is diffeomorphic to a disjoint union of cylinders.
The center of ℤ[𝕊ⁿ⁺¹] is the set of symmetric polynomials in 𝕟 commuting transposition-sums
Authors: Moran Gadi
Published: June 2012

Let

S

n
+
1

{S_{n + 1}}

be the symmetric group on the

n
+
1

n + 1

symbols

0
,
1
,
2
,
…
,
n

0,1,2, \ldots ,n

. We show that the center of the group-ring

Z

[

S

n
+
1

]

\mathbb {Z}[{S_{n + 1}}]

coincides with the set of symmetric polynomials with integral coefficients in the

n
n

elements

s
1

,
…
,

s
n

∈

Z

[

S

n
+
1

]

{s_1}, \ldots ,{s_n} \in \mathbb {Z}[{S_{n + 1}}]

, where

s
k

=

∑

0
≤
i
>
k

(
i
,
k
)

{s_k} = \sum \nolimits _{0 \leq i > k} {(i,k)}

is a sum of

k
k

transpositions,

k
=
1
,
…
,
n

k = 1, \ldots ,n

. In particular, every conjugacy-class-sum of

S

n
+
1

{S_{n + 1}}

is a symmetric polynomial in

s
1

,
…
,

s
n

{s_1}, \ldots ,{s_n}

.
QED domains and NED sets in \overline{𝐑}ⁿ
Authors: Yang Shan Shuang
Published: June 2012

This paper contributes to the theory of quasiextremal distance (or

QED

{\text {QED}}

) domains. We associate with every

QED

{\text {QED}}

domain

D
D

two

QED

{\text {QED}}

constants

M
(
D
)

M(D)

and

M

∗

(
D
)

{M^{\ast } }(D)

and exhibit how these constants reflect the geometry of

D
D

. For example, we give a geometric characterization for

QED

{\text {QED}}

domains

D
D

with

M

∗

(
D
)
=
2

{M^{\ast }}(D) = 2

and obtain some sharp estimates of

QED

{\text {QED}}

constants

M
(
D
)

M(D)

and

M

∗

(
D
)

{M^{\ast } }(D)

for different kinds of domains.
A topological method for bounded solutions of nonautonomous ordinary differential equations
Authors: Ward James R.
Published: June 2012

The existence of bounded solutions to nonlinear nonautonomous ordinary differential equations is studied. This is done by associating the given equation to nonlinear autonomous ones by means of a family of skew-product flows related by homotopy. The existence of a bounded solution to the original differential equation is then related to the nontriviality of a certain Conley index associated with the autonomous differential equations. The existence of nontrivial bounded solutions is also considered. The differential equations studied are perturbations of homogeneous ones.
An asymptotic estimate for heights of algebraic subspaces
Authors: Thunder Jeffrey Lin
Published: June 2012

We count the number of subspaces of affine space with a given dimension defined over an algebraic number field with height less than or equal to

B
B

. We give an explicit asymptotic estimate for the number of such subspaces as

B
B

goes to infinity, where the constants involved depend on the classical invariants of the number field (degree, discriminant, class number, etc.). The problem is reformulated as an estimate for the number of lattice points in a certain bounded domain.
Justification of multidimensional single phase semilinear geometric optics
Authors: Joly Jean-Luc , Rauch Jeffrey
Published: June 2012

For semilinear strictly hyperbolic systems

L
u
=
f
(
x
,
u
)

Lu= f(x,u)

, we construct and justify high frequency nonlinear asymptotic expansions of the form
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="u Superscript epsilon Baseline left-parenthesis x right-parenthesis tilde sigma-summation Underscript j greater-than-or-equal-to 0 Endscripts epsilon Superscript j Baseline upper U Subscript j Baseline left-parenthesis x comma phi left-parenthesis x right-parenthesis slash epsilon comma upper L u Superscript epsilon Baseline minus f left-parenthesis x comma u Superscript epsilon Baseline right-parenthesis tilde 0 period">

u
ε

(
x
)
∼

∑

j

≥

0

ε
j

U
j

(
x
,
φ

(
x
)

/

ε

,

L

u
ε

−
f
(
x
,

u
ε

)
∼
0
.

{u^\varepsilon }(x)\sim \sum \limits _{j\, \geq \,0} {{\varepsilon ^j}{U_j}(x,\varphi \,(x)/\varepsilon }, \quad L{u^\varepsilon } - f(x,{u^\varepsilon })\sim 0 .

\]
The study of the principal term of such expansions is called nonlinear geometric optics in the applied literature. We show (i) formal expansions with periodic profiles

U
j

{U_j}

can be computed to all orders, (ii) the equations for the profiles from (i) are solvable, and (iii) there are solutions of the exact equations which have the formal series as high frequency asymptotic expansion.
Accessible points of hereditarily decomposable chainable continua
Authors: Minc Piotr , Transue W. R. R.
Published: June 2012

In this paper it is proven that a chainable continuum

X
X

can be embedded in the plane in such a way that every point is accessible from its complement if and only if it is Suslinean. An example is shown of an hereditarily decomposable chainable continuum which cannot be embedded in the plane in such a way that each endpoint is accessible.
On the singular cardinal hypothesis
Authors: Mitchell W. J.
Published: June 2012

We use core model theory to obtain the following lower bounds to the consistency strength for the failure of the Singular Cardinal Hypothesis: Suppose that

κ
\kappa

is a singular strong limit cardinal such that

2
κ

>

κ
+

{2^\kappa } > {\kappa ^ + }

. Then there is an inner model

K
K

such that

o
(
κ
)
=

κ

+
+

o(\kappa ) = {\kappa ^{ + + }}

in

K
K

if

κ
\kappa

has uncountable cofinality, and

∀
α
>
κ
∃
ν
>
κ
o
(
κ
)
⩾
ν

\forall \alpha > \kappa \exists \nu > \kappa o(\kappa ) \geqslant \nu

in

K
K

otherwise.
Anomalies associated to the polar decomposition of 𝐺𝐿(𝑛,𝐶)
Authors: Rosenberg Steven
Published: June 2012

Let

D
D

be a selfadjoint elliptic differential operator on a hermitian bundle over a compact manifold. For positive

D
D

, the variation of the functional determinant of

D
D

under positive definite hermitian gauge transformations is calculated. This corresponds to computing a gauge anomaly in the nonunitary directions of the polar decomposition of the frame bundle

GL

(
E
)

{\text {GL}}(E)

. The variation of the eta invariant for general

D
D

is also calculated. If

D
D

is not selfadjoint, the integrand in the heat equation proof of the Atiyah-Singer Index Theorem is interpreted as an anomaly for

D

∗

D

{D^{\ast } }D

. In particular, the gauge anomaly for semiclassical Yang-Mills theory is computed.
Delta methods in enveloping algebras of Lie superalgebras
Authors: Bergen Jeffrey , Passman D. S.
Published: June 2012

Let

L
L

be a Lie superalgebra over a field

K
K

of characteristic

≠
2

\ne 2

. We define
\[

Δ
(
L
)
=
{
l
∈
L

|

dim
K

[
L
,
l
]
>
∞
}
.

\Delta (L) = \{ l \in L|{\dim _K}[L,l] > \infty \}.

\]
Then

Δ
(
L
)

\Delta (L)

is a Lie ideal of

L
L

and is restricted if

L
L

is restricted.

Δ
(
L
)

\Delta (L)

is the Lie superalgebra analog of the Lie delta ideal, used by the authors in the study of enveloping rings, and also of the finite conjugate center of a group, used in the study of group algebras and crossed products. In this paper we examine

U
(
L
)

U(L)

, where depending upon

char
⁡
K

\operatorname {char}K

,

U
(
L
)

U(L)

denotes either the enveloping algebra or the restricted enveloping algebra of

L
L

. We show that

Δ
(
L
)

\Delta (L)

controls certain properties of

U
(
L
)

U(L)

. Specifically, we consider semiprimeness, primeness, almost constants, almost centralizers, central closures, and the Artinian condition.
Admissible boundary values of bounded holomorphic functions in wedges
Authors: Forstnerič Franc
Published: June 2012

If

M
⊂

C

N

M \subset {\mathbb {C}^N}

is a generic Cauchy-Riemann manifold and

W

⊂

C

N

\mathcal {W} \subset {\mathbb {C}^N}

is a wedge domain with edge

M
M

, then every bounded holomorphic function on

W

\mathcal {W}

has an admissible limit at almost every point of

M
M

. Moreover, if a holomorphic function

f
f

on

W

\mathcal {W}

has a distribution boundary value

(
bv

f
)

(\operatorname {bv}\;f)

on

M
M

that is a bounded measurable function, then

f
f

is bounded on every finer wedge near

M
M

, and its admissible limit equals

(
bv

f
)
(
p
)

(\operatorname {bv}\;f)(p)

at almost every point

p
∈
M

p \in M

.
Generalized second-order derivatives of convex functions in reflexive Banach spaces
Authors: Do Chi Ngoc
Published: June 2012

Generalized second-order derivatives introduced by Rockafellar in finite-dimensional spaces are extended to convex functions in reflexive Banach spaces. Parallel results are shown in the infinite-dimensional case. A result that plays an important role in applications is that the generalized second-order differentiability is preserved under the integral sign.
A recurrent nonrotational homeomorphism on the annulus
Authors: Fokkink Robbert J. , Oversteegen Lex G.
Published: June 2012

We construct an area- and orientation-preserving recurrent diffeomorphism on the annulus without periodic points, which is not conjugate to a rotation. The mapping is, however, semiconjugate to an irrational rotation of a circle. Our example is a counterexample to the Birkhoff Conjecture.
An upper bound for the least dilatation
Authors: Bauer Max
Published: June 2012

We given an upper bound for the least dilatation arising from a pseudo-Anosov map of a closed surface of genus greater or equal to three.
Harmonic maps into hyperbolic 3-manifolds
Authors: Minsky Yair N.
Published: June 2012

High-energy degeneration of harmonic maps of Riemann surfaces into a hyperbolic

3
3

-manifold target is studied, generalizing results of [M1] in which the target is two-dimensional. The Hopf foliation of a high-energy map is mapped to an approximation of its geodesic representative in the target, and the ratio of the squared length of that representative to the extremal length of the foliation in the domain gives an estimate for the energy. The images of harmonic maps obtained when the domain degenerates along a Teichmüller ray are shown to converge generically to pleated surfaces in the geometric topology or to leave every compact set of the target when the limiting foliation is unrealizable.
The classification of spinors under 𝐺𝑆𝑝𝑖𝑛₁₄ over finite fields
Authors: Zhu Xiao-Wei
Published: June 2012

The spinors of a

14
14

-dimensional vector space

V
V

are studied with respect to the group

GSpin

14

\operatorname {GSpin}_{14}

of the

14
14

-dimensional vector space

V
V

over finite fields

F

q

{{\mathbf {F}}_q}

. Results are given as follows: (1) the decomposition of the space of spinors into

GSpin

14

\operatorname {GSpin}_{14}

-equivalence classes or "orbits" over

F

q

{{\mathbf {F}}_q}

, (2) the structure of the fixer of

GSpin

14

\operatorname {GSpin}_{14}

for each orbit as an

F

q

{{\mathbf {F}}_q}

-group.
The strong maximal function on a nilpotent group
Authors: Christ Michael
Published: June 2012

An analogue of the strong maximal function of Jessen, Marcinkiewicz, and Zygmund is shown to be bounded on

L
p

{L^p}

, for all

p
>
1

p > 1

, on a nilpotent Lie group.
Algebra for Heckoid groups
Authors: Riley Robert
Published: June 2012

We introduce an infinite collection of (Laurent) polynomials associated with a

2
2

-bridge knot or link normal form

K
=
(
α
,
β
)

K = (\alpha ,\beta )

. Experimental evidence suggests that these "Heckoid polynomials" define the affine representation variety of certain groups, the Heckoid groups, for

K
K

. We discuss relations which hold in the image of the generic representation for each polynomial. We show that, with a certain change of variable, each Heckoid polynomial divides the nonabelian representation polynomial of

L
L

, where

L
L

belongs to an infinite collection of

2
2

-bridge knots/links determined by

K
K

and the Heckoid polynomial. Finally, we introduce a "precusp polynomial" for each

2
2

-bridge knot normal form, and show it is the product of two (possibly reducible) non-constant polynomials. We are preparing a sequel on the Heckoid groups and the evidence for some of the geometrical assertions stated in the introduction.
Toeplitz and Hankel operators on Bergman spaces
Authors: Stroethoff Karel , Zheng De Chao
Published: June 2012

In this paper we consider Toeplitz and Hankel operators on the Bergman spaces of the unit ball and the polydisk in

C

n

{\mathbb {C}^n}

whose symbols are bounded measurable functions. We give necessary and sufficient conditions on the symbols for these operators to be compact. We study the Fredholm theory of Toeplitz operators for which the corresponding Hankel operator is compact. For these Toeplitz operators the essential spectrum is computed and shown to be connected. We also consider symbols that extend to continuous functions on the maximal ideal space of

H
∞

(
Ω
)

{H^\infty }(\Omega )

; for these symbols we describe when the Toeplitz or Hankel operators are compact.
Mixed groups
Authors: Hill Paul , Megibben Charles
Published: June 2012

As the culmination of a series of several papers, we establish here a combinatorial characterization of Warfield groups (that is, direct summands of simply presented abelian groups) in terms of knice subgroups—a refinement of the concept of nice subgroup appropriate to the study of groups containing elements of infinite order. Central to this theory is the class of

k
k

-groups, those in which

0
0

is a knice subgroup, and the proof that this class is closed under the formation of knice isotype subgroups. In particular, a direct summand of a

k
k

-group is a

k
k

-group. As an application of our Axiom

3
3

characterization of Warfield groups, we prove that

k
k

-groups of cardinality

ℵ
1

{\aleph _1}

have sequentially pure projective dimension

≤
1

\leq 1

; or equivalently, if

H
H

is a knice isotype sub-group of the Warfield group

G
G

with

|

G

/

H

|

=

ℵ
1

|G/H| = {\aleph _1}

, then

H
H

is itself a Warfield group.
The conormal derivative problem for equations of variational type in nonsmooth domains
Authors: Lieberman Gary M.
Published: June 2012

It is well known that elliptic boundary value problems in smooth domains have smooth solutions, but if the domain is, say,

C
1

{C^1}

, the solutions need not be Lipschitz. Recently Korevaar has identified a class of Lipschitz domains, in which solutions of the capillary problem are Lipschitz assuming the contact angle relates correctly to the geometry of the domain. Lipschitz bounds for more general boundary value problems in the same class of domains are proved. Applications to variational inequalities are also considered.
Σ_{𝑛} definable sets without Σ_{𝑛} induction
Authors: Chong C. T. , Mourad K. J.
Published: June 2012

We prove that the Friedberg-Muchnik Theorem holds in all models of

Σ
1

{\Sigma _1}

collection under the base theory

P
−

+
I

Σ
0

{P^- } + I{\Sigma _0}

. Generalizations to higher dimensional analogs are discussed. We also study the splitting of r.e. sets in these weak models of arithmetic.
Pseudo-isotopies of irreducible 3-manifolds
Authors: Kiralis Jeff
Published: June 2012

It is shown that a certain subspace of the space of all pseudo-isotopies of any irreducible

3
3

-manifold is connected. This subspace consists of those pseudo-isotopies corresponding to

1
1

-parameter families of functions which have nondegenerate critical points of index

1
1

and

2
2

only and which contain no slides among the

2
2

-handles. Some of the techniques developed are used to prove a weak four-dimensional

h
h

-cobordism theorem.
Generalized group presentation and formal deformations of CW complexes
Authors: Brown Richard A.
Published: June 2012

A Peiffer-Whitehead word system

W

\mathcal {W}

, or generalized group presentation, consists of generators, relators (words of order

2
2

), and words of higher order

n
n

that represent elements of a free crossed module

(
n
=
3
)

(n = 3)

or a free module

(
n
>
3
)

(n > 3)

. The

P
n

{P_n}

-equivalence relation on word systems generalizes the extended Nielsen equivalence relation on ordinary group presentations. Word systems, called homotopy readings, can be associated with any connected

CW

{\text {CW}}

complex

K
K

by removing a maximal tree and selecting one generator or word per cell, via relative homotopy. Given homotopy readings

W

1

{\mathcal {W}_1}

and

W

2

{\mathcal {W}_2}

of finite

CW

{\text {CW}}

complexes

K
1

{K_1}

and

K
2

{K_2}

respectively, we show that

W

1

{\mathcal {W}_1}

is

P
n

{P_n}

-equivalent to

W

2

{\mathcal {W}_2}

if and only if

K
1

{K_1}

formally

(
n
+
1
)

(n + 1)

-deforms to

K
2

{K_2}

. This extends results of P. Wright (1975) and W. Metzler (1982) for the case

n
=
2

n = 2

. For

n
≥
3

n \geq 3

, it follows that

W

1

{\mathcal {W}_1}

is

P
n

{P_n}

-equivalent to

W

2

{\mathcal {W}_2}

if and only if

K
1

{K_1}

and

K
2

{K_2}

have the same simple homotopy type.
On the self-intersections of foliation cycles
Authors: Mitsumatsu Yoshihiko
Published: June 2012

The existence of a transverse invariant measure imposes a strong restriction on the transverse complexity of a foliated manifold. The homological self-intersection of the corresponding foliation cycle measures the complexity around its support. In the present paper, the vanishing of the self-intersection is proven under some regularity condition on the measure.
Intersection theory of linear embeddings
Authors: Keel Sean
Published: June 2012

We study intersection theoretic properties of subschemes defined by ideal sheaves of linear type in particular their behavior with respect to blowups and segre classes.
Semilinear evolution equations in Banach spaces with application to parabolic partial differential equations
Authors: Rankin Samuel M.
Published: June 2012

A theory for a class of semilinear evolution equations in Banach spaces is developed which when applied to certain parabolic partial differential equations with nonlinear terms in divergence form gives strong solutions even for nondifferentiable data.
On mapping class groups of contractible open 3-manifolds
Authors: Myers Robert
Published: June 2012

Let

W
W

be an irreducible, eventually end-irreducible contractible open

3
3

-manifold other than

R

3

{{\mathbf {R}}^3}

, and let

V
V

be a "good" exhaustion of

W
W

. Let

H

(
W
;
V
)

\mathcal {H}(W;V)

be the subgroup of the mapping class group

H

(
W
)

\mathcal {H}(W)

which is "eventually carried by

V
V

." This paper shows how to compute

H

(
W
;
V
)

\mathcal {H}(W;V)

in terms of the mapping class groups of certain compact

3
3

-manifolds associated to

V
V

. The computation is carried out for a genus two example and for the classical genus one example of Whitehead. For these examples

H

(
W
)
=

H

(
W
;
V
)

\mathcal {H}(W) = \mathcal {H}(W;V)

.
Volumes of vector fields on spheres
Authors: Pedersen Sharon L.
Published: June 2012

In this paper we study the problem: What is the unit vector field of smallest volume on an odd-dimensional sphere? We exhibit on each sphere a unit vector field with singularity which has exceptionally small volume on spheres of dimension greater than four. We conjecture that this volume is the infimum for volumes of bona fide unit vector fields, and is only achieved by the singular vector field. We generalize the construction of the singular vector field to give a family of cycles in Stiefel manifolds, each of which is a smooth manifold except for one singular point. Except for some low-dimensional cases, the tangent cones at these singular points are volume-minimizing; and half of the cones are nonorientable. Thus, we obtain a new family of nonorientable volume-minimizing cones.
The value semigroups of prime divisors of the second kind in 2-dimensional regular local rings
Authors: Noh Sunsook
Published: June 2012

In this paper, it is shown that the value semigroup of a prime divisor of the second kind on a

2
2

-dimensional regular local ring is symmetric. Further, a necessary and sufficient condition for two prime divisors of the second kind on a

2
2

-dimensional regular local ring to have the same value semigroup is obtained.
Decidable discriminator varieties from unary classes
Authors: Willard Ross
Published: June 2012

Let

K

\mathcal {K}

be a class of (universal) algebras of fixed type.

K

t

{\mathcal {K}^t}

denotes the class obtained by augmenting each member of

K

\mathcal {K}

by the ternary discriminator function

(
t
(
x
,
y
,
z
)
=
x

(t(x,y,z) = x

if

x
≠
y
,
t
(
x
,
x
,
z
)
=
z
)

x \ne y,t(x,x,z) = z)

, while

∨
(

K

t

)

\vee ({\mathcal {K}^t})

is the closure of

K

t

{\mathcal {K}^t}

under the formation of subalgebras, homomorphic images, and arbitrary Cartesian products. For example, the class of Boolean algebras is definitionally equivalent to

∨
(

K

t

)

\vee ({\mathcal {K}^t})

where

K

\mathcal {K}

consists of a two-element algebra whose only operations are the two constants. Any equationally defined class (that is, variety) of algebras which is equivalent to some

∨
(

K

t

)

\vee ({\mathcal {K}^t})

is known as a discriminator variety. Building on recent work of S. Burris, R. McKenzie, and M. Valeriote, we characterize those locally finite universal classes

K

\mathcal {K}

of unary algebras of finite type for which the first-order theory of

∨
(

K

t

)

\vee ({\mathcal {K}^t})

is decidable.
Generalizations of the wave equation
Authors: Ash J. Marshall , Cohen Jonathan , Freiling C. , Rinne Dan
Published: June 2012

The main result of this paper is a generalization of the property that, for smooth

u
u

,

u

x
y

=
0

{u_{xy}} = 0

implies

(
∗
)

(\ast )

\[

u
(
x
,
y
)
=
a
(
x
)
+
b
(
y
)
.

u(x,y) = a(x) + b(y).

\]
Any function having generalized unsymmetric mixed partial derivative identically zero is of the form

(
∗
)

(\ast )

. There is a function with generalized symmetric mixed partial derivative identically zero not of the form

(
∗
)

(\ast )

, but

(
∗
)

(\ast )

does follow here with the additional assumption of continuity. These results connect to the theory of uniqueness for multiple trigonometric series. For example, a double trigonometric series is the

L
2

{L^2}

generalized symmetric mixed partial derivative of its formal

(
x
,
y
)

(x,y)

-integral.
Weighted norm inequalities for homogeneous singular integrals
Authors: Duoandikoetxea Javier
Published: June 2012

We prove weighted norm inequalities for homogeneous singular integrals when only a size condition is assumed on the restriction of the kernel to the unit sphere. The same results hold for the operator obtained by modifying the centered Hardy-Littlewood maximal operator over balls with a degree zero homogeneous function and also for the maximal singular integral.
Asymptotic homotopy cycles for flows and Π₁ de Rham theory
Authors: Benardete Diego , Mitchell John
Published: June 2012

We define the asymptotic homotopy of trajectories of flows on closed manifolds. These homotopy cycles take values in the

2
2

-step nilpotent Lie group which is associated to the fundamental group by means of Malcev completion. The cycles are an asymptotic limit along the orbit of the product integral of a Lie algebra valued

1
1

-form. Propositions 5.1-5.7 show how the formal properties of our theory parallel the properties of the asymptotic homology cycles of Sol Schwartzman. In particular, asymptotic homotopy is an invariant of topological conjugacy, and, in certain cases, of topological equivalence. We compute the asymptotic homotopy of those measure-preserving flows on Heisenberg manifolds which lift from the torus

T
2

{T^2}

(Theorem 8.1), and then show how this invariant distinguishes up to topological equivalence certain of these flows which are indistinguishable homologically (Theorem 9.1). We also compute the asymptotic homotopy of those geodesic flows for Heisenberg manifolds which come from left invariant metrics on the Heisenberg group (Example 8.1), and then show how this invariant distinguishes up to topological conjugacy certain of these flows which are indistinguishable homologically.
A short proof of Zheludev’s theorem
Authors: Gesztesy F. , Simon B.
Published: June 2012

We give a short proof of Zheludev’s theorem that states the existence of precisely one eigenvalue in sufficiently distant spectral gaps of a Hill operator subject to certain short-range perturbations. As a by-product we simultaneously recover Rofe-Beketov’s result about the finiteness of the number of eigenvalues in essential spectral gaps of the perturbed Hill operator. Our methods are operator theoretic in nature and extend to other one-dimensional systems such as perturbed periodic Dirac operators and weakly perturbed second order finite difference operators. We employ the trick of using a selfadjoint Birman-Schwinger operator (even in cases where the perturbation changes sign), a method that has already been successfully applied in different contexts and appears to have further potential in the study of point spectra in essential spectral gaps.
Algebraic cycles and the Hodge structure of a Kuga fiber variety
Authors: Gordon B. Brent
Published: June 2012

Let

A
~

\tilde A

denote a smooth compactification of the

k
k

-fold fiber product of the universal family

A
1

→
M

{A^1} \to M

of elliptic curves with level

N
N

structure. The purpose of this paper is to completely describe the algebraic cycles in and the Hodge structure of the Betti cohomology

H

∗

(

A
~

,

Q

)

{H^{\ast } }(\tilde A,\mathbb {Q})

of

A
~

\tilde A

, for by doing so we are able (a) to verify both the usual and generalized Hodge conjectures for

A
~

\tilde A

; (b) to describe both the kernel and the image of the Abel-Jacobi map from algebraic cycles algebraically equivalent to zero (modulo rational equivalence) into the Griffiths intermediate Jacobian; and (c) to verify Tate’s conjecture concerning the algebraic cycles in the étale cohomology

H

et

∗

(

A
~

⊗

Q

¯

,

Q

l

)

H_{{\text {et}}}^{\ast } (\tilde A \otimes \bar {\mathbb {Q}},{\mathbb {Q}_l})

. The methods used lead also to a complete description of the Hodge structure of the Betti cohomology

H

∗

(

E
k

,

Q

)

{H^{\ast } }({E^k},\mathbb {Q})

of the

k
k

-fold product of an elliptic curve

E
E

without complex multiplication, and a verification of the generalized Hodge conjecture for

E
k

{E^k}

.
𝑇1 theorems for Besov and Triebel-Lizorkin spaces
Authors: Han Y.-S. , Hofmann Steve
Published: June 2012

We give simple proofs of the

T
1

T1

theorem in the general context of Besov spaces and (weighted) Triebel-Lizorkin spaces. Our approach yields some new results for kernels satisfying weakened regularity conditions, while also recovering previously known results.
Super efficiency in vector optimization
Authors: Borwein J. M. , Zhuang D.
Published: June 2012

We introduce a new concept of efficiency in vector optimization. This concept, super efficiency, is shown to have many desirable properties. In particular, we show that in reasonable settings the super efficient points of a set are norm-dense in the efficient frontier. We also provide a Chebyshev characterization of super efficient points for nonconvex sets and a scalarization theory when the underlying set is convex.
Kac-Moody Lie algebras, spectral sequences, and the Witt formula
Authors: Kang Seok-Jin
Published: June 2012

In this work, we develop a homological theory for the graded Lie algebras, which gives new information on the structure of the Lorentzian Kac-Moody Lie algebras. The technique of the Hochschild-Serre spectral sequences offers a uniform method of studying the higher level root multiplicities and the principally specialized affine characters of Lorentzian Kac-Moody Lie algebras.
Determinants of Laplacians on the space of conical metrics on the sphere
Authors: King Hala Khuri
Published: June 2012

On a compact surface with smooth boundary, the determinant of the Laplacian associated to a smooth metric on the surface (with Dirichlet boundary conditions if the boundary is nonempty) is a well-defined isospectral invariant. As a function on the moduli space of such surfaces, it is a smooth function whose boundary behavior in certain cases is well understood; see [OPS and K]. In this paper, we restrict ourselves to a certain class of singular metrics on closed surfaces called conical metrics. We show that the determinant of the associated Laplacian is still well defined and that it is a real analytic function on a suitably restricted subset of the space of conical metrics on the sphere.
Induced connections on 𝑆¹-bundles over Riemannian manifolds
Authors: D’Ambra G.
Published: June 2012

Let

(
V
,
g
)

(V,g)

and

(
W
,
h
)

(W,h)

be Riemannian manifolds and consider two

S
1

{S^1}

-bundles

X
→
V

X \to V

and

Y
→
W

Y \to W

with connections

Γ
\Gamma

on

X
X

and

∇
\nabla

on

Y
Y

respectively. We study maps

X
→
Y

X \to Y

which induce both connections and metrics. Our study relies on Nash’s implicit function theorem for infinitesimally invertible differential operators. We show, for the case when

Y
→
W
=

C

P
q

Y \to W = {\mathbf {C}}{P^q}

is the Hopf bundle, that if

2
q
≥
n
(
n
+
1
)

/

2
+
3
n

2q \geq n(n + 1)/2 + 3n

then there exists a nonempty open subset in the space of

C
∞

{C^\infty }

-pairs

(
g
,
Γ
)

(g,\Gamma )

on

V
V

which can be induced from

(
h
,
∇
)

(h,\nabla )

on

C

P
Q

{\mathbf {C}}{P^Q}

.
Local integrability of Mizohata structures
Authors: Hounie Jorge , Malagutti Pedro
Published: June 2012

In this work we study the local integrability of strongly pseudoconvex Mizohata structures of rank

n
>
2

n > 2

(and co-rank

1
1

). These structures are locally generated in an appropriate coordinate system

(

t
1

,
…
,

t
n

,
x
)

({t_1}, \ldots ,{t_n},x)

by flat perturbations of Mizohata vector fields
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper M Subscript j Baseline equals StartFraction partial-differential Over partial-differential t Subscript j Baseline EndFraction minus i t Subscript j Baseline StartFraction partial-differential Over partial-differential x EndFraction">

M
j

=

∂

∂

t
j

−
i

t
j

∂

∂
x

{M_j} = \frac {\partial } {{\partial {t_j}}} - i{t_j}\frac {\partial } {{\partial x}}

,

j
=
1
,
…
,
n

j = 1, \ldots ,n

. For this, we first prove the global integrability of small perturbations of the structure generated by

∂

∂

z
¯

+

σ
1

∂

∂
z

\frac {\partial } {{\partial \bar z}} + {\sigma _1}\frac {\partial } {{\partial z}}

,

∂

∂

θ

n
−
1

+

σ
j

∂

∂
z

\frac {\partial } {{\partial {\theta _{n - 1}}}} + {\sigma _j}\frac {\partial } {{\partial z}}

,

j
=
2
,
…
,
n

j = 2, \ldots ,n

, defined over a manifold

C

×
S

{\mathbf {C}} \times S

, where

S
S

is simply connected.
Ergodic theory for Markov fibred systems and parabolic rational maps
Authors: Aaronson Jon , Denker Manfred , Urbański Mariusz
Published: June 2012

A parabolic rational map of the Riemann sphere admits a non atomic

h
h

-conformal measure on its Julia set where

h
=

h =

the Hausdorff dimension of the Julia set and satisfies

1

/

2
>
h
>
2

1/2 > h > 2

. With respect to this measure the rational map is conservative, exact and there is an equivalent

σ
\sigma

-finite invariant measure. Finiteness of the measure is characterised. Central limit theorems are proved in the case of a finite invariant measure and return sequences are identified in the case of an infinite one. A theory of Markov fibred systems is developed, and parabolic rational maps are considered within this framework.
Complex multiplication cycles and a conjecture of Beĭlinson and Bloch
Authors: Schoen Chad
Published: June 2012

A generalization of the conjecture of Birch and Swinnerton-Dyer is investigated using complex multiplication cycles on a particular Kuga fiber variety. A weak finiteness result consistent with the conjecture is proved. The image of complex multiplication cycles under the Abel-Jacobi map is computed explicitly. The results provide numerical evidence supporting the conjecture. They also give evidence for a relationship between complex multiplication cycles and a modular form of weight

5

/

2

5/2

and raise questions for further investigation.
Equiconvergence theorems for Fourier-Bessel expansions with applications to the harmonic analysis of radial functions in Euclidean and non-Euclidean spaces
Authors: Colzani Leonardo , Crespi Antonio , Travaglini Giancarlo , Vignati Marco
Published: June 2012

We shall prove an equiconvergence theorem between Fourier-Bessel expansions of functions in certain weighted Lebesgue spaces and the classical cosine Fourier expansions of suitable related functions. These weighted Lebesgue spaces arise naturally in the harmonic analysis of radial functions on euclidean spaces and we shall use the equiconvergence result to deduce sharp results for the pointwise almost everywhere convergence of Fourier integrals of radial functions in the Lorentz spaces

L

p
,
q

(

R

n

)

{L^{p,q}}({{\mathbf {R}}^n})

. Also we shall briefly apply the above approach to the study of the harmonic analysis of radial functions on noneuclidean hyperbolic spaces.
𝜔-chaos and topological entropy
Authors: Li Shi Hai
Published: June 2012

We present a new concept of chaos,

ω
\omega

-chaos, and prove some properties of

ω
\omega

-chaos. Then we prove that

ω
\omega

-chaos is equivalent to positive entropy on the interval. We also prove that

ω
\omega

-chaos is equivalent to the definition of chaos given by Devaney on the interval.
Noncommutative Köthe duality
Authors: Dodds Peter G. , Dodds Theresa K.-Y. , de Pagter Ben
Published: June 2012

Using techniques drawn from the classical theory of rearrangement invariant Banach function spaces we develop a duality theory in the sense of Köthe for symmetric Banach spaces of measurable operators affiliated with a semifinite von Neumann algebra equipped with a distinguished trace. A principal result of the paper is the identification of the Köthe dual of a given Banach space of measurable operators in terms of normality.