on the relative reflexivity of finitely generated modules of operators let s be a von neumann algebra on a hilbert space z with commutant and centre w for each subspace e of s let ref r be the space of all b e w such that xby 0 for all x y e s satisfying xyy o if ref y the space y is called s reflexive if s z and 5 is an algebra containing the identity operator s reflexivity reduces to the usual reflexivity in operator theory the main result of the paper is the following if y is one dimensional or if r is arbitrary finitedimensional but s has no central portions of type in for n 1 then the space is s reflexive and the space is z reflexive where the bar denotes the closure in the ultraweak operator topology if s is a factor then is closed in the weak operator topology for each finite dimensional subspace 5 of s

classification of irreducible weight modules over higher rank virasoro algebras let g be a rank n additive subgroup of c and vir g the corresponding virasoro algebra of rank n in the present paper irreducible weight modules with finite dimensional weight spaces over vir g are completely determined there are two different classes of them one class consists of simple modules of intermediate series whose weight spaces are all 1 dimensional the other is constructed by using intermediate series modules over a virasoro subalgebra of rank n 1 the classification of such modules over the classical virasoro algebra was obtained by o mathieu in 1992 using a completely different approach

approximately spectrum preserving maps let x and y be superreflexive complex banach spaces and let b x and b y be the banach algebras of all bounded linear operators on x and y respectively if a bijective linear map b x b y almost preserves the spectra then it is almost multiplicative or anti multiplicative furthermore in the case where x y is a separable complex hilbert space such a map is a small perturbation of an automorphism or an anti automorphism

derivation simple algebras and the structures of lie algebras of witt type abstract we classify all the pairs of a commutative associative algebra with an identity element and its finite dimensional locally finite abelian derivation subalgebra such that the commutative associative algebra is derivation simple with respect to the derivation subalgebra over an algebraically closed field with characteristic 0 such pairs are the fundamental ingredients for constructing simple lie algebras of cartan type moreover we determine the isomorphism classes of the simple lie algebras of witt type the structure space of these algebras is given explicitly

multiplicity one representations of divergence free lie algebras abstract divergence free lie algebras also known as the special lie algebras of cartan type are lie algebras of volume preserving transformation groups they are simple in generic case dokovic and zhao found a certain graded generalization of them in this paper we classify all the irreducible and indecomposable multiplicity one modules of the simple generalized divergence free lie algebras

derivations and central extensions of finitely generated graded lie algebras abstract some general results concerning derivations of finitely generated lie algebras are established these are employed in order to determine the derivations and central extensions of kac moody lie algebras

the apostol fialkow formula for elementary operators on banach spaces abstract let a a 1 a n and b 1 b n be n tuples of bounded linear operators on a banach space e the corresponding elementary operator e a b is the map s n i 1 a i sb i on l e and e a b denotes the induced operator s n i 1 a i sb i on the calkin algebra c e l e k e here t t k e for t l e we establish that if e has a 1 unconditional basis then dist e a b w c e e a b dist e a b w l e for all elementary operators e a b on l e where w stands for the weakly compact operators there is equality throughout if e l p 1 p canad j math 38 1986 1485 1524 which they proved for e l 2 using the non commutative weyl von neumann theorem due to voiculescu by contrast our arguments are based on subsequence techniques from banach space theory as a byproduct we obtain a positive answer to the generalized fong sourour conjecture for a large class of banach spaces we also explicitly compute the norm of the generalized derivation s as sb on c l 2 this improves a result due to fong and show that the resulting formula fails to hold on c l p

automorphisms and verma modules for generalized schrodinger virasoro algebras abstract let f be a field of characteristic 0 g an additive subgroup of f f satisfying g and 2 g we define a class of infinite dimensional lie algebras which are called generalized schrodinger virasoro algebras and denoted by gsv g in this paper the automorphism group and irreducibility of verma modules for gsv g are completely determined

the spectral picture of la rb abstract let a and b be commuting n tuples of operators on a hilbert space h and let l a r b be the 2 n tuple of left and right multiplications induced by a and b on l h we show that t l a r b l h t a h t b h te l a r b l h te a h t b h t a h te b h and ind l a r b 1 n ind a ind b whenever a and b are fredholm similar results hold for the restrictions of l a r b to norm ideals in l h giving in particular the spectral picture of a i i b on h h a s fainstein working independently has announced versions of these results for banach spaces

derivations isomorphisms and second cohomology of generalized witt algebras generalized witt algebras over a field f of characteristic 0 were defined by kawamoto about 12 years ago using different notations from kawamoto s we give an essentially equivalent definition of generalized witt algebras w w a t over f where the ingredients are an abelian group a a vector space t over f and a map t a k which is linear in the first variable and additive in the second one in this paper the derivations of any generalized witt algebra w w a t with the right kernel of being 0 are explicitly described the isomorphisms between any two simple generalized witt algebras are completely determined and the second cohomology group h2 w f for any simple generalized witt algebra is computed the derivations the automorphisms and the second cohomology groups of some special generalized witt algebras have been studied by several other authors as indicated in the references

elementary operators on antiliminal c algebras we establish the equivalence of the following three properties of a c algebra a a every positive elementary operator on a is completely positive b the norm and the cb norm coincide for every elementary operator on a c a is an extension of an antiliminal c algebra by an abelian one

subconvex bounds for hecke maass forms on compact arithmetic quotients of semisimple lie groups let h be a semisimple algebraic group k a maximal compact subgroup of g h mathbb r and gamma subset h mathbb q a congruence arithmetic subgroup in this paper we generalize existing subconvex bounds for hecke maass forms on the locally symmetric space gamma backslash g k to corresponding bounds on the arithmetic quotient gamma backslash g for cocompact lattices using the spectral function of an elliptic operator the bounds obtained extend known subconvex bounds for automorphic forms to non trivial k types yielding such bounds for new classes of automorphic representations they constitute subconvex bounds for eigenfunctions on compact manifolds with both positive and negative sectional curvature we also obtain new subconvex bounds for holomorphic modular forms in the weight aspect

derivations and invariant forms of jordan and alternative tori jordan and alternative tori are the coordinate algebras of extended affine lie algebras of types a 1 and a 2 in this paper we show that the derivation algebra of a jordan torus is a semidirect product of the ideal of inner derivations and the subalgebra of central derivations in the course of proving this result we investigate derivations of the more general class of division graded jordan and alternative algebras we also describe invariant forms of these algebras

on factorial states of operator algebras results for the factorial state space of a c algebra a which are analogous to results of glimm ann of math 72 1960 216 244 73 1961 572 612 tomiyama and takesaki tohoku math j 2 13 1961 498 523 for the pure state space it is shown that a is prime if and only if the type i factorial states are dense in the state space it follows that every factorial state is a w limit of type i factorial states the factorial state space of a von neumann algebra is determined and it is shown that if a is unital and acts non degenerately on a hilbert space then the factorial state space of the generated von neumann algebra restricts precisely to the factorial state space of a it is shown that the set of factorial states is w compact if and only if a is unital liminal and has hausdorff primitive ideal space

a characterization of positive linear maps and criteria of entanglement for quantum states let h and k be finite or infinite dimensional complex hilbert spaces a characterization of positive completely bounded normal linear maps from into is given which particularly gives a characterization of positive elementary operators including all positive linear maps between matrix algebras this characterization is then applied to give a representation of quantum channels operations between infinite dimensional systems a necessary and sufficient criterion of separability is given which shows that a state on h k is separable if and only if i 0 for all positive finite rank elementary operators examples of ncp and indecomposable positive linear maps are given and are used to recognize some entangled states that cannot be recognized by the ppt criterion and the realignment criterion