ISOMORPHISMS AND DERIVATIONS IN C*-ALGEBRAS

In this article, we prove the Hyers-Ulam-Rassias stability of the following Cauchy-Jensen functional inequality：‖f （x） ＋ f （y） ＋ 2f （z） ＋ 2f （w）‖ ≤‖ 2f x ＋ y2 ＋ z ＋ w ‖（0.1）This is applied to investigate isomorphisms between C＊-algebras, Lie C＊-algebras and JC＊-algebras, and derivations on C＊-algebras, Lie C＊-algebras and JC＊-algebras, associated with the Cauchy-Jensen functional equation 2f （x ＋ y/2 ＋ z ＋ w） = f（x） ＋ f（y） ＋ 2f（z） ＋ 2f（w）.

ISOMETRIC ISOMORPHISMS OF TRIANGULAR BANACH ALGEBRAS

Let A and B be Banach algebras.Let M be a Banach A,B module with bounded 1.Then T=AM 0B is a Banach algebra with the usual operations and the norm AM 0B=‖A‖+‖M‖+‖B‖.Such an algebra is called a triangular Banach algebra.In this paper the isometric isomorphisms of triangular Banach algebras are characterized.

ISOMORPHISMS OF VARIABLE HARDY SPACES ASSOCIATED WITH SCHRÖDINGER OPERATORS

Let L:=-△+V be the Schrodinger operator on R^(n)with n≥3,where V is a non-negative potential satisfying△^(-1)(V)∈L^(∞)(R^(n)).Let w be an L-harmonic function,determined by V,satisfying that there exists a positive constantδsuch that,for any x∈Rn,0<δ≤w(x)≤1.Assume that p(·):R^(n)→(0,1]is a variable exponent satisfying the globally log-Hölder continuous condition.In this article,the authors show that the mappings HL^(p)(·))(R^(n))■f■wf∈H^(p)(·)(R^(n))and HL^(p(·))(R^(n))■f■(-△)^(1/2)L^(-1/2)(f)∈H^(p(·))(R^(n))are isomorphisms between the variable Hardy spaces HL^(p(·))(R^(n)),associated with L,and the variable Hardy spaces H^(p(·))(R^(n)).

ISOMORPHISMS OF CIRCULANT DIGRAPHS OF DEGREE 3

In this paper, we introduce a new approach to characterize the isomor-phisms of circulant digraphs. In terms of this method, we completely determine theisomorphic classes of circulant digraphs of degree 3. In particular, we characterizethose circulant digraphs of degree 3 which don't satisfy Adam's conjecture.

Characterizations of Isomorphisms by Multiplicative Maps on Operator Algebras

In this paper, we discuss some multiplicative preservers and give some characterizations of isomorphisms or conjugate isomorphisms on β(X), where β(X) denotes the algebra of all bounded linear operators on a Banach space X.

Eventually homological isomorphisms and Gorenstein projective modules

We prove that a certain eventually homological isomorphism between module categories induces triangle equivalences between their singularity categories,Gorenstein defect categories and stable categories of Gorenstein projective modules.Furthermore,we show that the Auslander-Reiten conjecture and the Gorenstein symmetry conjecture can be reduced by eventually homological isomorphisms.Applying these results to arrow removal and vertex removal,we describe the Gorenstein projective modules over some non-monomial algebras and verify the Auslander-Reiten conjecture for certain algebras.

Isomorphisms of Cubic Cayley Graphs on Dihedral Groups and Sparse Circulant Matrices

We show that,up to isomorphism,there is a unique non-CI connected cubic Cayley graph on the dihedral group of order 2n for each even number n≥4.This answers in the negative the question of Li whether all connected cubic Cayley graphs are CI-graphs(Discrete Math.,256,301-334(2002)).As an application,a formula is derived for the number of isomorphism classes of connected cubic Cayley graphs on dihedral groups,which generalises the earlier formula of Huang et al.dealing with the particular case when n is a prime(Acta Math.Sin.,Engl.Ser.,33,996-1011(2017)).As another application,a short proof is also given for a result on sparse circulant matrices obtained by Wiedemann and Zieve(arXiv preprint,(2007)).

On the Proof of the Contradiction of Set Theory

The article is devoted to proving the inconsistency of set theory arising from the existence of strange trees. All steps of the proof rely on common informal set-theoretic reasoning, but they take into account the prohibitions that were introduced into axiomatic set theories in order to overcome the difficulties encountered by the naive Cantor set theory. Therefore, in fact, the article is about proving the inconsistency of existing axiomatic set theories, in particular, the ZFC theory.

ISOMORPHISMS BETWEEN ENDOMORPHISM RINGS OF FREE MODULES

In this paper we give the following main results: (ⅰ) Let F(?) and G(?) be two free modules. Then F(?) and G(?) are semi-linearly isomorphic if and only if End F(?) and End G(?) are strictly isomorphic. (ⅱ) We give a new method to generalize the Bolla theorem in 1985 which gave a categorical description for isomorphism between End F(?) and End G(?). (ⅲ) The Wolfson theorem is a corollary of our theorem.

Lifting of Isomorphisms Between Elementary Linear Groups

Let R and A be commutative rings with identity, and m and n be integers ≥3. Consider when and how an isomorphism E_m(R)E_n(A) can be lifted to an isomorphism between the corresponding Steinberg groups. It was proved that, if E_m(R) is isomorphic to E_n(A) then m=n (cf. Ref. [1]). When n≥4, every isomorphism E_n(R)E_n(A) is of the standard type, and it can be naturally and uniquely lifted to an isomorphism from St_n(R) to St_n(A) (cf. Refs. [1] and [2]). However, the case n=3 is different from that n≥4,

The Isomorphisms of Orthogonal Groups over Local Rings

1. Introduction Since O’Meara worked out the automorphisms of orthogonal groups Ωn(V) over fields in [4] by using well-known residual space method, many results about the isomorphisms and automorphisms of orthogonal groups over integral domains have been achieved. Refer to O’Meara, Hahn for example. B. R. McDonald, in [12], determined the automorphisms of O(V) over local rings with 2 a unit by using involutions.

ISOMORPHISMS OF GL_3 OVER COMMUTATIVE RINGS

In this paper, we discuss the necessary and sufficient conditions in which there exist exceptional isomorphisms between E3（A） and E3（R） and between GL3（A） and GL3（R） for commutative rings A and R. A counterexample shows that two rings that are not isomorphic may have isomorphic tinear groups. This partly solves an open problem posed at the conference on abstract homomorphisms of algebraic groupsrs.

Ball-covering property of Banach spaces that is not preserved under linear isomorphisms

By a ball-covering B of a Banach space X, we mean that it is a collection of open balls off the origin whose union contains the sphere of the unit ball of X. The space X is said to have a ball-covering property, if it admits a ball-covering consisting of countably many balls. This paper, by constructing the equivalent norms on l~∞, shows that ball-covering property is not invariant under isomorphic mappings, though it is preserved under such mappings if X is a Gateaux differentiability space; presents that this property of X is not heritable by its closed subspaces; and the property is also not preserved under quotient mappings.

Derivations and Isomorphisms of Certain Reflexive Operator Algebras

In this paper, we will prove that every derivation of completely distributive subspace lattice (CDS)algebras on Banach space is automatically continuous. This is new even in the Hilbert space case. As an application of this result, we obtain that every additive derivation of nest algebras on Banach spaces is inner. We will also prove that every isomorphism between nest algebras on Banach space is automatically continuous, and in addition, is spatial.

On the isomorphisms of the character rings

By considering the Galois action and the group action,we give the relation of two isomorphism character rings on the arbitrary field K with CharK = 0.Our results generalize Saksonov's theorem.

Isomorphisms of fiber spaces over Teichmüller spaces

We will be mainly concerned with some important fiber spaces over Teichmüller spaces, including the Bers fiber space and Teichmüller curve, establishing an isomorphism theorem between "punctured" Teichmüller curves and determining the biholomorphic isomorphisms of these fiber spaces.

On isomorphisms of integral table algebras

For integral table algebras with integral table basis T, we can consider integral R-algebra RT over a subring R of the ring of the algebraic integers. It is proved that an R-algebra isomorphism between two integral table algebras must be an integral table algebra isomorphism if it is compatible with the so-called normalizings of the integral table algebras.

Isomorphisms and Automorphisms of Generalized Semi-Cayley Graphs

In this paper we propose the concept of generalized semi-Cayley graphs, which is a combination of semi-Cayley graphs and generalized Cayley graphs. We study the isomorphisms and automorphisms of generalized semi-Cayley graphs and other related properties.

UHF-ALGEBRAS AND *-ISOMORPHISMS

The following problem is discussed: If μ is an AF-algebra, A and B are two C-algebras, x(A) and x(B) are the unit balls of μ A and μ B respectively, and there is an affine isomorphism from X(A) onto x(B), when are A and B isomorphic? This problem was inspired by K-theory of C*-algebras. If μ is a UHP-algebra of type {m^p}, an orientation on x(A) and x(B), i. e., an action of the special group of μ, is introduced. Then it is obtained that if the affine isomorphism commutes with the group action then A and B are isomorphic.

Isomorphisms between the coherent models of the lambda-calculus

It is proved that there exists a formula of first-order logic with only one non-logical symbol, a binary function symbol Ap signifying application, which uniformly defines inclusion in all BF(E)-models Some definability results give an isomorphism between the group of bi-stable Ap -automorphisms of A and the group of permutations of A; it also implies that each BF(E)-model is determined, up to isomorphism, by the cardinal of its set of atoms.