共查询到20条相似文献,搜索用时 15 毫秒
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T. W. Dawson J. F. Feinstein 《Proceedings of the American Mathematical Society》2003,131(9):2831-2839
We examine the condition that a complex Banach algebra has dense invertible group. We show that, for commutative algebras, this property is preserved by integral extensions. We also investigate the connections with an old problem in the theory of uniform algebras.
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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
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In 2003 Dawson and Feinstein asked whether or not a Banach function algebra with dense invertible group can have a proper Shilov boundary. We give an example of a uniform algebra showing that this can happen, and investigate the properties of such algebras. We make some remarks on the topological stable rank of commutative, unital Banach algebras. In particular, we prove that whenever is approximately regular.
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Frederic W Shultz 《Journal of Functional Analysis》1979,31(3):360-376
Alfsen, Shultz, and Størmer have defined a class of normed Jordan algebras called JB-algebras, which are closely related to Jordan algebras of self-adjoint operators. We show that the enveloping algebra of a JB-algebra can be identified with its bidual. This is used to show that a JB-algebra is a dual space iff it is monotone complete and admits a separating set of normal states; in this case the predual is unique and consists of all normal linear functionals. Such JB-algebras (“JBW-algebras”) admit a unique decomposition into special and purely exceptional summands. The special part is isomorphic to a weakly closed Jordan algebra of self-adjoint operators. The purely exceptional part is isomorphic to C(X, M38) (the continuous functions from X into M38). 相似文献
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M. A. Berdikulov 《Siberian Advances in Mathematics》2013,23(3):175-179
We prove martingale ergodic theorems for Jordan Banach algebras. 相似文献
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In this article, we construct a commutative unital Banach algebra, in which the property is true for the invertible elements, but cannot be extended to the whole algebra. 相似文献
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S. Giotopoulos 《Journal of Mathematical Analysis and Applications》2002,270(1):129-142
This paper provides an abstract characterization of quasitriangular algebras of operators on a separable Hilbert space. The main tool used is the (purely algebraic) concept of a single element. An element s of an algebra A is called single element of A if whenever asb=0 for some a, b in A, at least one of as,sb is zero. A part of this work is of independent interest and this is an attempt to determine an involution in a Banach algebra. 相似文献
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We consider a wide class of unital involutive topological algebras provided with aC
*-norm and which are inverse limits of sequences of unital involutive Banach algebras; these algebra sare taking a prominent position in noncommutative differential geometry, where they are often called unital smooth algebras. In this paper we prove that the group of invertible elements of such a unital solution smooth algebra and the subgroup of its unitary elements are regular analytic Fréchet-Lie groups of Campbell-Baker-Hausdorff type and fulfill a nice infinite-dimensional version of Lie's second fundamental theorem. 相似文献
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N. Jacobson 《Mathematische Annalen》1958,136(4):375-386
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Heinrich Raubenheimer 《Czechoslovak Mathematical Journal》2010,60(3):589-596
We characterize elements in a semisimple Banach algebra which are quasinilpotent equivalent to maximal finite rank elements. 相似文献
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M. S. Sgibnev 《Mathematical Notes》2013,93(5-6):763-765
Classical theorems concerning invertibility conditions for elements of Banach algebras of measures are generalized. 相似文献