共查询到20条相似文献,搜索用时 15 毫秒
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O. V. Lopushanskii 《Ukrainian Mathematical Journal》1991,43(2):130-133
Continuity conditions of one-parametric semigroups in locally convex algebras of general form are studied.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 2, pp. 154–158, February, 1991. 相似文献
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Helmut H. Schaefer 《Acta Mathematica》1962,107(1-2):125-173
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Edoardo Vesentini 《中国科学A辑(英文版)》2005,48(1):32-46
The Gleason-Kahane-Zelazko theorem characterizes the continuous homomorphism of an associative, locally multiplicatively convex, sequentially complete algebra A into the field ? among all linear forms on A. This characterization will be applied along two different directions. In the case in which A is a commutative Banach algebra, the theorem yields the representation of some classes of continuous linear maps A : A→ A as weighted composition operators, or as composition operators when A is a continuous algebra endomorphism. The theorem will then be applied to explore the behaviour of continuous linear forms on quasi-regular elements, when A is either the algebra of all Hilbert-Schmidt operators or a Hilbert algebra. 相似文献
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Edoardo Vesentini 《中国科学A辑(英文版)》2005,48(Z1)
The Gleason-Kahane-Zelazko theorem characterizes the continuous homo-morphism of an associative, locally multiplicatively convex, sequentially complete algebra A into the field C among all linear forms on A. This characterization will be applied along two different directions. In the case in which A is a commutative Banach algebra, the theorem yields the representation of some classes of continuous linear maps A:A→A as weighted composition operators, or as composition operators when A is a continuous algebra endomorphism. The theorem will then be applied to explore the behaviour of continuous linear forms on quasi-regular elements, when A is either the algebra of all Hilbert-Schmidt operators or a Hilbert algebra. 相似文献
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Subhash J Bhatt 《Proceedings Mathematical Sciences》1985,94(2-3):71-91
Consideration of quotient-bounded elements in a locally convexGB *-algebra leads to the study of properGB *-algebras viz those that admit nontrivial quotient-bounded elements. The construction and structure of such algebras are discussed. A representation theorem for a properGB *-algebra representing it as an algebra of unbounded Hilbert space operators is obtained in a form that unifies the well-known Gelfand-Naimark representation theorem forC *-algebra and two other representation theorems forb *-algebras (also calledlmc *-algebras), one representinga b *-algebra as an algebra of quotient bounded operators and the other as a weakly unbounded operator algebra. A number of examples are discussed to illustrate quotient-bounded operators. An algebra of unbounded operators constructed out of noncommutativeL p-spaces on a regular probability gauge space and the convolution algebra of periodic distributions are analyzed in detail; whereas unbounded Hilbert algebras andL w-integral of a measurable field ofC *-algebras are discussed briefly. 相似文献
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Martin Grensing 《Journal of Functional Analysis》2012,263(8):2170-2204
Using an appropriate notion of locally convex Kasparov modules, we show how to induce isomorphisms under a large class of functors on the category of locally convex algebras; examples are obtained from spectral triples. Our considerations are based on the action of algebraic K-theory on these functors, and involve compatibility properties of the induction process with this action, and with Kasparov-type products. This is based on an appropriate interpretation of the Connes–Skandalis connection formalism. As an application, we prove Bott periodicity and a Thom isomorphism for algebras of Schwartz functions. As a special case, this applies to the theories kk for locally convex algebras considered by Cuntz. 相似文献
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Let G be a locally compact group with a weight function ω. Recently, we have shown that the Banach space L0∞ (G,1/ω) can be identified with the strong dual of L1(G, ω)equipped with some locally convex topologies τ. Here we use this duality to introduce an Arens multiplication on (L1(G, ω), τ)**, and prove that the topological center of (L1(G, ω), τ)** is (L1(G, ω); this enables us to conclude that (L1(G, ω), τ) is Arens regular if and only if G is discrete. We also give a characterization for Arens regularity of L0∞ (G, 1/ω)1.
Received: 8 March 2005 相似文献
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This paper is concerned with the algebraic K-theory of locally convex C-algebras stabilized by operator ideals, and its comparison with topological K-theory. We show that if L is locally convex and J a Fréchet operator ideal, then all the different variants of topological K-theory agree on the completed projective tensor product , and that the obstruction for the comparison map to be an isomorphism is (absolute) algebraic cyclic homology. We prove the existence of an exact sequence (Theorem 6.2.1)We show that cyclic homology vanishes in the case when J is the ideal of compact operators and L is a Fréchet algebra whose topology is generated by a countable family of sub-multiplicative seminorms and admits an approximate right or left unit which is totally bounded with respect to that family (Theorem 8.3.3). This proves the generalized version of Karoubi's conjecture due to Mariusz Wodzicki and announced in his paper [M. Wodzicki, Algebraic K-theory and functional analysis, in: First European Congress of Mathematics, Vol. II, Paris, 1992, in: Progr. Math., vol. 120, Birkhäuser, Basel, 1994, pp. 485-496].We also consider stabilization with respect to a wider class of operator ideals, called sub-harmonic. Every Fréchet ideal is sub-harmonic, but not conversely; for example the Schatten ideal Lp is sub-harmonic for all p>0 but is Fréchet only if p?1. We prove a variant of the exact sequence above which essentially says that if A is a C-algebra and J is sub-harmonic, then the obstruction for the periodicity of K∗(AC⊗J) is again cyclic homology (Theorem 7.1.1). This generalizes to all algebras a result of Wodzicki for H-unital algebras announced in [M. Wodzicki, Algebraic K-theory and functional analysis, in: First European Congress of Mathematics, Vol. II, Paris, 1992, in: Progr. Math., vol. 120, Birkhäuser, Basel, 1994, pp. 485-496].The main technical tools we use are the diffeotopy invariance theorem of Cuntz and the second author (which we generalize in Theorem 6.1.6), and the excision theorem for infinitesimal K-theory, due to the first author. 相似文献
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Jun Kawabe 《Proceedings of the American Mathematical Society》1996,124(5):1513-1515
The purpose of this paper is to show that a theorem of A. Wisniewski remains valid without the approximation property.
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A. El Kinani 《Rendiconti del Circolo Matematico di Palermo》2004,53(3):407-416
We show that the convexified topology of a locally pseuod-convex algebra can be determined by an explicit family of seminorms.
A natural relationship between some properties of locally pseudo-convex algebras and the associated locally convex algebras
obtained by convexification is also established. 相似文献
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O. V. Belegradek 《Mathematical Notes》1989,46(5):831-834
Transited from Matematicheskie Zametki, Vol. 46, No. 5, pp. 3–8, November, 1989. 相似文献
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