jordan all derivable points in the algebra of all upper triangular matrices abstract let tm n be the algebra of all n n upper triangular matrices we say that l tm n is a jordan derivable mapping at g if st ts s t s t t s t s for any s t tm n with st g an element g tm n is called a jordan all derivable point of tm n if every jordan derivable linear mapping at g is a derivation in this paper we show that every element in tm n is a jordan all derivable point

multiplicative mappings at some points on matrix algebras let mn be the algebra of all n n matrices and let mn mn be a linear mapping we say that is a multiplicative mapping at g if st s t for any s t mn with st g fix g mn we say that g is an all multiplicative point if every multiplicative linear bijection at g with in in is a multiplicative mapping in mn where in is the unit matrix in mn we mainly show in this paper the following two results 1 if g mn with detg 0 then g is an all multiplicative point in mn 2 if is an multiplicative mapping at in then there exists an invertible matrix p mn such that either s psp 1 for any s mn or t pttrp 1 for any t mn

local holder regularity for solutions of elliptic systems in this note we prove local l p regularity for the highest order derivatives of an elliptic system of arbitrary order in nondivergence form where the coefficients of the principal part are taken in the space of sarason vanishing mean oscillation vmo lower order coefficients and the known term belong to suitable lebesgue spaces as

renormalization and localization expansions ii expectation values of the fluctuation measures this paper is a continuation of 5 the k 1 st renormalization transformation applied to a density k is studied further the new contributions to the effective action obtained in 5 are renormalized and their localization expansions are constructed this completes proofs of theorems 1 and 4 in 5

the variational problems for classical n vector models we prove existence and regularity properties of solutions of the variational problems introduced in the previous paper 1 for classical lattice n vector models these results form a basis of our renormalization group approach to low temperature expansions for the considered models

a low temperature expansion for classical n vector models iii a complete inductive description fluctuation integrals we give a complete inductive description of the effective densities generated by applications of the renormalization transformations to the densities of the classical n vector models described in the paper 1 and we formulate the main theorems of this sequence of papers this description includes now all the large field domains which we ve excluded from the discussions of 1 4 we apply the renormalization transformation to a density satisfying the inductive hypotheses we introduce large field small field partitions and we determine and analyze the fluctuation integrals in the general setting

higgs 2 3 quantum fields in a finite volume we consider a euclidean model of interacting scalar and vector fields in two and three dimensions and prove a lower bound for vacuum energy in a lattice approximation the bound is independent of a lattice spacing it is proved with the help of renormalization transformations in wilson kadanoff form it extends in principal also to generating functional for schwinger functions

derivable mappings at unit operator on nest algebras abstract let a be an operator subalgebra with the unit operator i in b h we say that a linear mapping from a into itself is a derivable mapping at i if st s t s t for any s t a with st i in this paper we show the following main result every strongly operator topology continuous derivable mapping at i on a nest algebra alg n is an inner derivation

all derivable points in matrix algebras abstract let m n be the algebra of all n n matrices we say that an element g m n is an all derivable point in m n if every derivable linear mapping at g i e st s t s t for any s t m n with st g is a derivation we mainly show in this paper that a matrix g is an all derivable point in m n if and only if g 0

characterizations of isomorphisms and derivations of some algebras abstract let be a zero product preserving bijective bounded linear map from a unital algebra a onto a unital algebra b such that 1 k we show that if a is a csl algebra on a hilbert space or a j lattice algebra on a banach space then there exists an isomorphism from a onto b such that k for a nest algebra a in a factor von neumann algebra we characterize the linear maps on a such that x y x y 0 for all x y a with x y 0

validity of the spin wave approximation for the free energy of the heisenberg ferromagnet we consider the quantum ferromagnetic heisenberg model in three dimensions for all spins s 1 2 we rigorously prove the validity of the spin wave approximation for the excitation spectrum at the level of the first non trivial contribution to the free energy at low temperatures our proof comes with explicit constructive upper and lower bounds on the error term it uses in an essential way the bosonic formulation of the model in terms of the holstein primakoff representation in this language the model describes interacting bosons with a hard core on site repulsion and a nearest neighbor attraction this attractive interaction makes the lower bound on the free energy particularly tricky the key idea there is to prove a differential inequality for the two particle density which is thereby shown to be smaller than the probability density of a suitably weighted two particle random process on the lattice

characterizations of derivations and jordan derivations on banach algebras abstract let a be an algebra and m be an a bimodule let x be in a and a m be a linear map which satisfies ab a b a b for all a b a with ab x it is shown that is a jordan derivation if is continuous and x is left or right invertible also it is shown that is a derivation if x is idempotent such that for m m the condition x a i x m 0 implies i x m 0 and the condition mx a i x 0 implies mx 0

spectrum preserving linear maps abstract let x and y be banach spaces we show that a spectrum preserving surjective linear map from b x to b y is either of the form t ata 1 for an isomorphism a of x onto y or the form t bt b 1 for an isomorphism b of x onto y

constructive field theory and applications perspectives and open problems in this paper we review many interesting open problems in mathematical physics which may be attacked with the help of tools from constructive field theory they could give work for future mathematical physicists trained with constructive methods well into the 21st century

the large field renormalization operation for classical n vector models a renormalization operation of the large field densities for the classical n vector models is constructed in this paper it allows to improve bounds of these densities and thus to prove all inductive hypotheses this completes the construction and analysis of the full renormalization group flow for these models the results will be used in the next paper to analyze the correlation functions

all derivable points in continuous nest algebras let a be an operator algebra on a hilbert space we say that an element g a is an all derivable point of a for the strong operator topology if every strong operator topology continuous derivable linear mapping at g i e st s t s t for any s t algn with st g is a derivation let n be a continuous nest on a complex and separable hilbert space h we show in this paper that every orthogonal projection operator p m 0 m n is an all derivable point of algn for the strong operator topology

the renormalization group according to balaban ii large fields this is an expository account of balaban s approach to the renormalization group the method is illustrated with a treatment of the ultraviolet problem for the scalar 4 model on a toroidal lattice in dimension d 3 in this paper we control the large field contribution to the partition function

interior estimates in morrey spaces for strong solutions to nondivergence form equations with discontinuous coefficients abstract let us consider the nondivergence form elliptic equation a ij u x i x j in this paper we show that if the known term belongs to the morrey space l p then the second derivatives of the w 2 p solution u belong to the same space next we derive a c 1 loc regularity result that is related to a recent work by caffarelli

additive maps derivable at some points on j subspace lattice algebras abstract let l be a j subspace lattice on a real or complex banach space dim x with x 2 and alg l be the associated j subspace lattice algebra let alg l alg l be an additive map it is shown that if is derivable at zero point i e ab a b a b whenever ab 0 then a a a a where is an additive derivation and is a scalar if is generalized derivable at zero point i e ab a b a b a i b whenever ab 0 then is a generalized derivation it is also shown that if x is complex then every linear map derivable at unit operator on alg l is a derivation

on a spectral characterization of rank one matrices abstract let a be an n n complex matrix with a 2 0 it is proved that a has rank one if and only if t a t ca t for every rank one matrix t and some fixed scalar c 0 or 1 the condition a 2 0 cannot be dropped in case n 4

multiscale formalism for correlation functions of fermions infrared analysis of the tridimensional gross neveu model we present a multiscale formalism for fermionic systems with a smooth uv cutoff establishing a trivial link between the correlation functions and the effective potential flow and study the k point truncated functions of the tridimensional gross neveu model a new efficient method is used to bound these correlation functions and show polynomial tree decay for long distances we are guided by a block lattice mechanism with a property of orthogonality between terms in different scales which leads to simple formulas for the correlations

on positive linear maps preserving invertibility theorem a positive linear map 4 between two c algebras is a jordan homomorphism if d preserves invertibility and the range of is a c algebra a counterexample is given for the case that the range of q is not assumed to be a c algebra this answers a question raised by b russo proc amer math sot 17

a low temperature expansion for classical n vector models ii renormalization group equations this paper continues the analysis of the low temperature expansions for classicaln vector models started in 1 a main part of it is a derivation of renormalization group equations and a construction of their solutions to do this we have to introduce a fluctuation integral connected with a next renormalization transformation and to make its preliminary analysis the results of the paper are summarized in theorems stating that the renormalization transformation preserves the space of densitites or actions described inductively in 1

all derivable points of operator algebras abstract let a be an operator subalgebra in b h where h is a hilbert space we say that an element z a is an all derivable point of a for the norm topology strongly operator topology etc if every norm topology strongly operator topology etc continuous derivable linear mapping at z i e st s t s t for any s t a with st z is a derivation in this paper we show that every invertible operator in the nest algebra alg n is an all derivable point of the nest algebra for the strongly operator topology we also prove that every nonzero element of the algebra of all 2 2 upper triangular matrixes is an all derivable point of the algebra

commutators and generalized local morrey spaces abstract in this paper we study the behavior of hardy littlewood maximal operator and the action of commutators in generalized local morrey spaces l m x 0 p r n and generalized morrey spaces m p r n

on jordan all derivable points of b h abstract let h be a hilbert space and b h the algebra of all bounded linear operators on h in this note we show that 0 is a generalized jordan all derivable point of b h if h is infinite dimensional for any hilbert space h we also show that i is a jordan all derivable point of b h