共查询到20条相似文献,搜索用时 15 毫秒
1.
Osamu Hatori 《Journal of Mathematical Analysis and Applications》2011,376(1):84-93
We prove that an isometry T between open subgroups of the invertible groups of unital Banach algebras A and B is extended to a real-linear isometry up to translation between these Banach algebras. While a unital isometry between unital semisimple commutative Banach algebras need not be multiplicative, we prove in this paper that if A is commutative and A or B are semisimple, then (T(eA))−1T is extended to an isometric real algebra isomorphism from A onto B. In particular, A−1 is isometric as a metric space to B−1 if and only if they are isometrically isomorphic to each other as metrizable groups if and only if A is isometrically isomorphic to B as a real Banach algebra; it is compared by the example of ?elazko concerning on non-isomorphic Banach algebras with the homeomorphically isomorphic invertible groups. Isometries between open subgroups of the invertible groups of unital closed standard operator algebras on Banach spaces are investigated and their general forms are given. 相似文献
2.
Let A be a unital C*-algebra of real rank zero and B be a unital semisimple complex Banach algebra. We characterize linear maps from A onto B preserving different essential spectral sets and quantities such as the essential spectrum, the (left, right) essential spectrum, the Weyl spectrum, the index and the essential spectral radius. 相似文献
3.
Kenneth J. Dykema 《Journal of Functional Analysis》2006,231(1):90-110
The S-transform is shown to satisfy a specific twisted multiplicativity property for free random variables in a B-valued Banach noncommutative probability space, for an arbitrary unital complex Banach algebra B. Also, a new proof of the additivity of the R-transform in this setting is given. 相似文献
4.
Let B(X) be the algebra of all bounded linear operators on a complex Banach space X. We give the concrete form of every unital surjective map φ on B(X) such that AB is a non-zero idempotent if and only if φ(A)φ(B) is for all A,B∈B(X) when the dimension of X is at least 3. 相似文献
5.
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 ψ from A onto B such that ?=kψ. For a nest algebra A in a factor von Neumann algebra, we characterize the linear maps on A such that δ(x)y+xδ(y)=0 for all x,y∈A with xy=0. 相似文献
6.
Let A and B be unital Banach algebras and let M be a unital Banach A,B-module. Forrest and Marcoux [6] have studied the weak amenability of triangular Banach algebra \(\mathcal{T} = \left[ {_B^{AM} } \right]\) and showed that T is weakly amenable if and only if the corner algebras A and B are weakly amenable. When \(\mathfrak{A}\) is a Banach algebra and A and B are Banach \(\mathfrak{A}\)-module with compatible actions, and M is a commutative left Banach \(\mathfrak{A}\)-A-module and right Banach \(\mathfrak{A}\)-B-module, we show that A and B are weakly \(\mathfrak{A}\)-module amenable if and only if triangular Banach algebra T is weakly \(\mathfrak{T}\)-module amenable, where \(\mathfrak{T}: = \{ [^\alpha _\alpha ]:\alpha \in \mathfrak{A}\} \). 相似文献
7.
Jean Esterle 《Journal of Functional Analysis》1980,36(3):273-286
We prove that a commutative unital Banach algebra which is a valuation ring must reduce to the field of complex numbers, which implies that every homomorphism from l∞ onto a Banach algebra is continuous. We show also that if b? [b Rad B]? for some nonnilpotent element b of the radical of a commutative Banach algebra B, then the set of all primes of B cannot form a chain, and we deduce from this result that every homomorphism from (K) onto a Banach algebra is continuous. 相似文献
8.
Jiankui Li 《Linear algebra and its applications》2010,432(1):5-322
For a commutative subspace lattice L in a von Neumann algebra N and a bounded linear map f:N∩algL→B(H), we show that if Af(B)C=0 for all A,B,C∈N∩algL satisfying AB=BC=0, then f is a generalized derivation. For a unital C∗-algebra A, a unital Banach A-bimodule M, and a bounded linear map f:A→M, we prove that if f(A)B=0 for all A,B∈A with AB=0, then f is a left multiplier; as a consequence, every bounded local derivation from a C∗-algebra to a Banach A-bimodule is a derivation. We also show that every local derivation on a semisimple free semigroupoid algebra is a derivation and every local multiplier on a free semigroupoid algebra is a multiplier. 相似文献
9.
Dmitry Goldstein 《Integral Equations and Operator Theory》1999,33(2):172-174
LetA denote a unital Banach algebra, and letB denote aC
*-algebra which is contained as a unital subalgebra inA. We prove thatB is inverse closed inA if the norms ofA andB coincide. This generalizes well known result about inverse closedness ofC
*-subalgebras inC
*-algebras. 相似文献
10.
On derivable mappings 总被引:1,自引:0,他引:1
Jiankui Li 《Journal of Mathematical Analysis and Applications》2011,374(1):311-322
A linear mapping δ from an algebra A into an A-bimodule M is called derivable at c∈A if δ(a)b+aδ(b)=δ(c) for all a,b∈A with ab=c. For a norm-closed unital subalgebra A of operators on a Banach space X, we show that if C∈A has a right inverse in B(X) and the linear span of the range of rank-one operators in A is dense in X then the only derivable mappings at C from A into B(X) are derivations; in particular the result holds for all completely distributive subspace lattice algebras, J-subspace lattice algebras, and norm-closed unital standard algebras of B(X). As an application, every Jordan derivation from such an algebra into B(X) is a derivation. For a large class of reflexive algebras A on a Banach space X, we show that inner derivations from A into B(X) can be characterized by boundedness and derivability at any fixed C∈A, provided C has a right inverse in B(X). We also show that if A is a canonical subalgebra of an AF C∗-algebra B and M is a unital Banach A-bimodule, then every bounded local derivation from A into M is a derivation; moreover, every bounded linear mapping from A into B that is derivable at the unit I is a derivation. 相似文献
11.
S. B. Tabaldyev 《Moscow University Mathematics Bulletin》2014,69(4):164-168
It is proved that if A = C(Ω), where Ω is an infinite metrizable compact space such that some finite-order iterated derived set of Ω is empty, then for every unital Banach algebra B the global dimensions and the bidimensions of the Banach algebras A \(\hat \otimes \) B and B are related as dg A \(\hat \otimes \) B = 2 + dg B and db A \(\hat \otimes \) B = 2 + db B. Thus, a partial extension of Selivanov’s result is obtained. 相似文献
12.
Bojan Magajna 《Journal of Mathematical Analysis and Applications》2009,350(1):252-255
We prove that if a unital Banach algebra A is the dual of a Banach space A? then the set of normal states is weak∗ dense in the set of all states on A. Further, normal states linearly span A?. 相似文献
13.
Zinaida A. Lykova 《代数通讯》2013,41(6):1779-1793
We prove that, for every natural number n, there exists a unital semisimple Banach star algebra Aand a closed star subalgebra Bof the centre of A, different from C, such that the global B-homological dimension and the B-homological bidimension of Aare both equal to n. The algebras Aand Bcan be taken to be function algebras. 相似文献
14.
Osamu Hatori Takeshi Miura Hiroyuki Takagi 《Journal of Mathematical Analysis and Applications》2007,326(1):281-296
Let T be a surjective map from a unital semi-simple commutative Banach algebra A onto a unital commutative Banach algebra B. Suppose that T preserves the unit element and the spectrum σ(fg) of the product of any two elements f and g in A coincides with the spectrum σ(TfTg). Then B is semi-simple and T is an isomorphism. The condition that T is surjective is essential: An example of a non-linear and non-multiplicative unital map from a commutative C*-algebra into itself such that σ(TfTg)=σ(fg) holds for every f,g are given. We also show an example of a surjective unital map from a commutative C*-algebra onto itself which is neither linear nor multiplicative such that σ(TfTg)⊂σ(fg) holds for every f,g. 相似文献
15.
Danrun Huang 《Integral Equations and Operator Theory》1992,15(3):454-469
LetA be a matrix over a complex commutative unital Banach algebra. We give necessary and sufficient conditions forA to have a generalized inverse. Moreover, if the Banach algebra has a symmetric involution, these are also necessary and sufficient conditions forA to admit the Moore-Penrose inverse.Partially supported by NSF Grant DMS-8802593 相似文献
16.
Yong-Soo Jung 《Journal of Mathematical Analysis and Applications》2008,339(1):108-114
Let A be a unital normed algebra and let M be a unitary Banach left A-module. If f:A→M is an approximate module left derivation, then f:A→M is a module left derivation. Moreover, if M=A is a semiprime unital Banach algebra and f(tx) is continuous in t∈R for each fixed x in A, then every approximately linear left derivation f:A→A is a linear derivation which maps A into the intersection of its center Z(A) and its Jacobson radical rad(A). In particular, if A is semisimple, then f is identically zero. 相似文献
17.
Ian Craw 《Journal of Functional Analysis》1978,27(2):170-178
Let A be a commutative unital Banach algebra with connected maximal ideal space X. We show that the Gelfand transform induces an isomorphism between the group of commutative Galois extensions of A with given finite Abelian Galois group, and the corresponding group of extensions of C(X). This result is applied, when X is sufficiently nice, to construct a separable projective finitely generated faithful Banach A-algebra whose maximal ideal space is a given finitely fibered covering space of X. 相似文献
18.
Let A be a Banach algebra with a faithful multiplication and ∗〈A∗A〉 be the quotient Banach algebra of A∗∗ with the left Arens product. We introduce a natural Banach algebra, which is a closed subspace of ∗〈A∗A〉 but equipped with a distinct multiplication. With the help of this Banach algebra, new characterizations of the topological centre Zt(∗〈A∗A〉) of ∗〈A∗A〉 are obtained, and a characterization of Zt(∗〈A∗A〉) by Lau and Ülger for A having a bounded approximate identity is extended to all Banach algebras. The study of this Banach algebra motivates us to introduce the notion of SIN locally compact quantum groups and the concept of quotient strong Arens irregularity. We give characterizations of co-amenable SIN quantum groups, which are even new for locally compact groups. Our study shows that the SIN property is intrinsically related to topological centre problems. We also give characterizations of quotient strong Arens irregularity for all quantum group algebras. Within the class of Banach algebras introduced recently by the authors, we characterize the unital ones, generalizing the corresponding result of Lau and Ülger. We study the interrelationships between strong Arens irregularity and quotient strong Arens irregularity, revealing the complex nature of topological centre problems. Some open questions by Lau and Ülger on Zt(∗〈A∗A〉) are also answered. 相似文献
19.
Bojan Kuzma 《Czechoslovak Mathematical Journal》2006,56(3):919-921
It is proved that a linear surjection Ф: A → B, which preserves noninvertibility between semisimple, unital, complex Banach algebras, is automatically injective. 相似文献
20.
Hongyan Zeng 《Linear algebra and its applications》2011,434(2):463-474
Let A be a Banach algebra with unity I and M be a unital Banach A-bimodule. A family of continuous additive mappings D=(δi)i∈N from A into M is called a higher derivable mapping at X, if δn(AB)=∑i+j=nδi(A)δj(B) for any A,B∈A with AB=X. In this paper, we show that D is a Jordan higher derivation if D is a higher derivable mapping at an invertible element X. As an application, we also get that every invertible operator in a nontrivial nest algebra is a higher all-derivable point. 相似文献