共查询到20条相似文献,搜索用时 15 毫秒
1.
The ideal space Id(A) of a Banach algebra A is studied as abitopological space Id(A), u, n, where u is the weakest topologyfor which all the norm functions I || a + I|| (with a A andI Id(A)) are upper semi-continuous, and n is the de Groot dualof u. When A is separable, nu is either a compact, metrizabletopology, or it is neither Hausdorff nor first countable. TAF-algebrasare shown to exhibit the first type of behaviour. Applicationsto Banach bundles (which motivate the study), and to PI-Banachalgebras, are given. 1991 Mathematics Subject Classification:46H10, 46J20. 相似文献
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In a previous paper, the second author introduced a compacttopology r on the space of closed ideals of a unital Banachalgebra A. If A is separable, then r is either metrizable orelse neither Hausdorff nor first countable. Here it is shownthat r is Hausdorff if A is C1[0, 1], but that if A is a uniformalgebra, then r is Hausdorff if and only if A has spectral synthesis.An example is given of a strongly regular, uniform algebra forwhich every maximal ideal has a bounded approximate identity,but which does not have spectral synthesis. 1991 MathematicsSubject Classification 46H10. 相似文献
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It is proved that the measure algebra M(G) of a locally compactgroup G is Connes-amenable if and only if G is amenable. 相似文献
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In this paper we extend the concept of amenable algebra given by Johnson in [ 3 ] to n-amenable algebra. We prove several properties which are extension of 1-amenable algebras appeared in [3] and [4], and we give a sufficient condition for a Banach algebra being 2- amenable. 相似文献
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Yi Ming Zou 《Advances in Applied Clifford Algebras》2009,19(1):147-153
The structures of the ideals of Clifford algebras which can be both infinite dimensional and degenerate over the real numbers
are investigated.
相似文献
9.
Anar Dosiev 《Integral Equations and Operator Theory》2008,61(3):341-364
In this paper we introduce regularities and subspectra in a unital noncommutative Banach algebra and prove that there is a
correspondence between them similar to the commutative case. This correspondence involves a radical on a class of Banach algebras
equipped with a subspectrum. Taylor and Slodkowski spectra for noncommutative tuples of bounded linear operators are the main
examples of subspectra in the noncommutative case.
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10.
Doklady Mathematics - In a complex Banach algebra that is not assumed to be commutative, nth-order linear differential equations with constant coefficients are considered. The corresponding... 相似文献
11.
Spectrum-Preserving Linear Mappings between Banach Algebras or Jordan-Banach Algebras 总被引:5,自引:0,他引:5
Spectrum-preserving linear mappings were studied for the firsttime by G. Frobenius [18]. He proved that a linear mapping 相似文献
12.
Luoyi Shi & Yujing Wu 《数学研究通讯:英文版》2014,30(1):1-10
Let $α$ be a flow on a Banach algebra$\mathcal{B}$, and $t → u_t$ a continuous function
from$\boldsymbol{R}$into the group of invertible elements of$\mathcal{B}$such that $u_sα_s(u_t) = u_{s+t}, s, t ∈ \boldsymbol{R}$.
Then $β_t$ = Ad$u_t ◦ α_t$, $t ∈ \boldsymbol{R}$ is also a flow on $\mathcal{B}$, where Ad$u_t(B) \triangleq u_tBu^{−1}_t$ for any $B ∈ \mathcal{B}$. $β$ is said to be a cocycle perturbation of $α$. We show that if $α$, $β$ are two
flows on a nest algebra (or quasi-triangular algebra), then $β$ is a cocycle perturbation
of $α$. And the flows on a nest algebra (or quasi-triangular algebra) are all uniformly
continuous. 相似文献
13.
We investigate the ideal structure of the Toeplitz algebra
of a totally ordered abelian group
. We show that the primitive ideals of
are parametrised by the disjoint union
of the duals
of the order ideals
of
, and identify the
hull-kernel topology on
when the chain of orderideals in
is isomorphic to a subset of
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By showing the existence of certain functions in A+ (the algebraof analytic functions in the unit disc with absolutely convergentTaylor series), we prove that if T is a power bounded operatoron a Banach space X, and x X satisfies Tx x, then
相似文献
16.
We show that several known facts concerning roots of matrices generalize to operator algebras and Banach algebras. We show for example that the so-called Newton, binomial, Visser, and Halley iterative methods converge to the root in Banach and operator algebras under various mild hypotheses. We also show that the ‘sign’ and ‘geometric mean’ of matrices generalize to Banach and operator algebras, and we investigate their properties. We also establish some other facts about roots in this setting. 相似文献
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Marcel Erné 《Applied Categorical Structures》2000,8(1-2):115-144
We introduce ideals, radicals and prime ideals in arbitrary algebras with at least one binary operation, and we show that various separation lemmas and prime ideal theorems are special instances of one general theorem which, in turn, is equivalent to the Boolean Prime Ideal Theorem (or Ultrafilter Principle). 相似文献
19.
Continuity of Lie Isomorphisms of Banach Algebras 总被引:1,自引:0,他引:1
We prove that if A and B are semisimple Banach algebras, thenthe separating subspace of every Lie isomorphism from A ontoB is contained in the centre of B. 1991 Mathematics SubjectClassification 17B40, 17B60, 46H40. 相似文献
20.
In the 1970s, a question of Kaplansky about discontinuous homomorphismsfrom certain commutative Banach algebras was resolved. Let Abe the commutative C*-algebra C(), where is an infinite compactspace. Then, if the continuum hypothesis (CH) be assumed, thereis a discontinuous homomorphism from C() into a Banach algebra[2, 7]. In fact, let A be a commutative Banach algebra. Then(with (CH)) there is a discontinuous homomorphism from A intoa Banach algebra whenever the character space A of A is infinite[3, Theorem 3] and also whenever there is a non-maximal, primeideal P in A such that |A/P|=20 [4, 8]. (It is an open questionwhether or not every infinite-dimensional, commutative Banachalgebra A satisfies this latter condition.) 1991 MathematicsSubject Classification 46H40. 相似文献