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1.
Aida Toma 《Rendiconti del Circolo Matematico di Palermo》2009,58(1):29-40
This paper proves a new integral representation theorem for powers of elements in locally m-convex algebras. It is shown that the conditions handled in this theorem are satisfied for any sequentially complete locally
m-convex Q-algebra. Various applications of this result concerning the spectrum, the spectral radius or the numerical radius are given.
相似文献
2.
Choonkil PARK Jian Lian CUI 《数学学报(英文版)》2007,23(11):1919-1936
Let X and Y be vector spaces. The authors show that a mapping f : X →Y satisfies the functional equation 2d f(∑^2d j=1(-1)^j+1xj/2d)=∑^2dj=1(-1)^j+1f(xj) with f(0) = 0 if and only if the mapping f : X→ Y is Cauchy additive, and prove the stability of the functional equation (≠) in Banach modules over a unital C^*-algebra, and in Poisson Banach modules over a unital Poisson C*-algebra. Let A and B be unital C^*-algebras, Poisson C^*-algebras or Poisson JC^*- algebras. As an application, the authors show that every almost homomorphism h : A →B of A into is a homomorphism when h((2d-1)^nuy) =- h((2d-1)^nu)h(y) or h((2d-1)^nuoy) = h((2d-1)^nu)oh(y) for all unitaries u ∈A, all y ∈ A, n = 0, 1, 2,....
Moreover, the authors prove the stability of homomorphisms in C^*-algebras, Poisson C^*-algebras or Poisson JC^*-algebras. 相似文献
3.
Jeffrey L. BOERSEMA 《数学学报(英文版)》2007,23(10):1827-1832
We prove analogs of the Kaplansky Density Theorem and the Kadison Transitivity Theorem for irreducible representations of a real C*-algebra on a real Hilbert space. Specifically, if a C*-algebra is acting irreducibly on a real Hilbert space, then the Hilbert space has either a real, complex, or quaternionic structure with respect to which the density and transitivity theorems hold. 相似文献
4.
Chun-Gil Park Hahng-Yun Chu Won-Gil Park Hee-Jeong Wee 《Czechoslovak Mathematical Journal》2005,55(4):1055-1065
It is shown that every almost linear Pexider mappings f, g, h from a unital C*-algebra
into a unital C*-algebra ℬ are homomorphisms when f(2
n
uy) = f(2
n
u)f(y), g(2
n
uy) = g(2
n
u)g(y) and h(2
n
uy) = h(2
n
u)h(y) hold for all unitaries u ∈
, all y ∈
, and all n ∈ ℤ, and that every almost linear continuous Pexider mappings f, g, h from a unital C*-algebra
of real rank zero into a unital C*-algebra ℬ are homomorphisms when f(2
n
uy) = f(2
n
u)f(y), g(2
n
uy) = g(2
n
u)g(y) and h(2
n
uy) = h(2
n
u)h(y) hold for all u ∈ {v ∈
: v = v* and v is invertible}, all y ∈
and all n ∈ ℤ.
Furthermore, we prove the Cauchy-Rassias stability of *-homomorphisms between unital C*-algebras, and ℂ-linear *-derivations on unital C*-algebras.
This work was supported by Korea Research Foundation Grant KRF-2003-042-C00008.
The second author was supported by the Brain Korea 21 Project in 2005. 相似文献
5.
6.
Let S be a pomonoid and I a proper right ideal of S. In a previous paper, using the amalgamated coproduct A(I) of two copies of
S
S over I, we were able to solve one of the problems posed in S. Bulman-Fleming et al. (Commun. Algebra 34:1291–1317, 2006). In the present paper, we investigate further flatness properties of A(I). We also solve another problem stated in the paper cited above. Namely, we determine the condition under which Rees factor
S-posets have property (P
w
).
Research supported by nwnu-kjcxgc-03-18. 相似文献
7.
Sh. A. Ayupov 《Functional Analysis and Its Applications》2004,38(4):302-304
Let R be a real AW
*-algebra, and suppose that its complexification M = R + iR is also a (complex) AW
*-algebra. We prove that R is of type I if and only if so is M.Translated from Funktsionalnyi Analiz i Ego Prilozheniya, Vol. 38, No. 4, pp. 79–81, 2004Original Russian Text Copyright © by Sh. A. Ayupov 相似文献
8.
Let A be a separable simple C*-algebra. For each ;) on A such that π(a) has a non-trivial invariant subspace in Hπ. 相似文献
9.
M. V. Shchukin 《Russian Mathematics (Iz VUZ)》2011,55(7):81-88
In this paper we consider n-homogeneous C*-algebras generated by idempotents. We prove that a finitely generated unital n-homogeneous (when n is greater than or equals 2) C*-algebra A can be generated by a finite set of idempotents if and only if the algebra A contains at least one nontrivial idempotent. 相似文献
10.
Florentina Chirte§ 《Central European Journal of Mathematics》2005,3(1):105-124
The aim of this paper is to define the localization LM
n
-algebra of an LM
n
—algebra L with respect to a topology F on L; in Section 5 we prove that the maximal LM
n
-algebra of fractions (defined in [3]) and the LM
n
-algebra of fractions relative to an Λ—closed system (defined in Section 2) are LM
n
-algebras of localization. 相似文献
11.
Thomas Vougiouklis 《数学学报(英文版)》2008,24(7):1067-1078
The hyperoperations, called theta-operations (δ), are motivated from the usual property, which the derivative has on the derivation of a product of functions. Using any map on a set, one can define δ-operations. In this paper, we continue our study on the δ-operations on groupoids, rings, fields and vector spaces or on the corresponding hyperstructures. Using δ-operations one obtains, mainly, Hwstructures, which form the largest class of the hyperstructures. For representation theory of hyperstructures, by hypermatrices, one needs special Hv-rings or Hy-fields, so these hyperstructures can be used. Moreover, we study the relation of these δ-structures with other classes of hyperstructures, especially with the Hv-structures. 相似文献
12.
We prove that for two elements x, y in a Hilbert C*-module V over a C*-algebra the C*-valued triangle equality |x + y| = |x| + |y| holds if and only if 〈x, y〉 = |x| |y|. In addition, if has a unit e, then for every x, y ∊ V and every ɛ > 0 there are contractions u, υ ∊ such that |x + y| ≦ u|x|u* + υ|y|υ* + ɛe.
相似文献
13.
Ján Jakubík 《Czechoslovak Mathematical Journal》2007,57(4):1099-1105
A generalized MV-algebra A is called representable if it is a subdirect product of linearly ordered generalized MV-algebras. Let S be the system of all congruence relations ϱ on A such that the quotient algebra A/ϱ is representable. In the present paper we prove that the system S has a least element.
This work was supported by Science and Technology Assistance Agency under Contract No AVPT-51-032002.
The work has been partially supported by the Slovak Academy of Sciences via the project Center of Excellence-Physics of Information
(grant I/2/2005). 相似文献
14.
J.C. FERRANDO S. MOLL 《数学学报(英文版)》2007,23(9):1593-1600
In this paper, we show, among other results, that if X is a [separable] locally compact space X [satisfying the first countability axiom] then the space Cc (X) has countable tightness [if and only if it has bounding tightness] if and only if it is Frechet-Urysohn, if and only if Cc (X) contains a dense (LM) subspace and if and only if X is a-compact. 相似文献
15.
Maria Joiţa 《Czechoslovak Mathematical Journal》2004,54(3):727-737
In this paper the tensor products of Hilbert modules over locally C
*-algebras are defined and their properties are studied. Thus we show that most of the basic properties of the tensor products of Hilbert C
*-modules are also valid in the context of Hilbert modules over locally C
*-algebras. 相似文献
16.
17.
A mistake concerning the ultra LI-ideal of a lattice implication algebra is pointed out, and some new sufficient and necessary conditions for an LI-ideal to be an ultra LI-ideal are given. Moreover, the notion of an LI-ideal is extended to MTL-algebras, the notions of a (prime, ultra, obstinate, Boolean) LI-ideal and an ILI-ideal of an MTL-algebra are introduced, some important examples are given, and the following notions are proved to be equivalent in MTL-algebra: (1) prime proper LI-ideal and Boolean LI-ideal, (2) prime proper LI-ideal and ILI-ideal, (3) proper obstinate LI-ideal, (4) ultra LI-ideal.
This work was supported by the Zhejiang Provincial Natural Science Foundation of China (Grant No. Y605389) and K. C. Wong
Magna Fund in Ningbo University. 相似文献
18.
O. H. Cheikh 《Rendiconti del Circolo Matematico di Palermo》2000,49(2):307-312
In a locallyA-convex algebra (E, τ) we consider the associatedm-convex topologym(τ). We show that the completion ofE with respect tom(τ) is always a locallyA-convex algebra contained in the complete locally convex space obtained from (E, τ). The topologym(τ) is also used to characterize locally boundedly multiplicatively convex algebras among locallyA-convex ones.
相似文献
19.
Choonkil Baak Mohammad Sal Moslehian 《Bulletin of the Brazilian Mathematical Society》2007,38(1):115-127
We introduce the concept of θ-derivations on JB*-triples and prove the Hyers–Ulam-Rassias stability of θ-derivations on JB*-triples. We deal with the Hyers-Ulam-Rassias stability that was first introduced by Th. M. Rassias in the paper “On the
stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297–300”.
The first author was supported by Korea Research Foundation Grant KRF-2005-070-C00009. 相似文献
20.
For given a graph H, a graphic sequence π = (d
1, d
2,..., d
n) is said to be potentially H-graphic if there is a realization of π containing H as a subgraph. In this paper, we characterize the potentially (K
5 − e)-positive graphic sequences and give two simple necessary and sufficient conditions for a positive graphic sequence π to
be potentially K
5-graphic, where K
r is a complete graph on r vertices and K
r-e is a graph obtained from K
r by deleting one edge. Moreover, we also give a simple necessary and sufficient condition for a positive graphic sequence
π to be potentially K
6-graphic.
Project supported by National Natural Science Foundation of China (No. 10401010). 相似文献