共查询到20条相似文献,搜索用时 15 毫秒
1.
Let
be a locally compact group. Consider the Banach algebra
, equipped with the first Arens multiplication, as well as the
algebra LUC
, the dual of the space of bounded left uniformly
continuous functions on
, whose product extends the convolution in
the measure algebra M
. We present (for the most interesting case
of a non-compact group) completely different - in particular,
direct - proofs and even obtain
sharpened versions of
the results, first proved by Lau-Losert in [9] and Lau in
[8], that the topological centres of the latter algebras
precisely are
and M
, respectively. The special interest of
our new approach lies in the fact that it shows a fairly general pattern
of solving the topological centre problem for various kinds of Banach
algebras; in particular, it avoids the use of any measure theoretical
techniques. At the same time, deriving both results in perfect
parallelity, our method reveals the nature of their close relation.Received: 1 January 2002 相似文献
2.
S.W. Drury 《Linear algebra and its applications》2011,435(2):323-329
We present an effective algorithm for estimating the norm of an operator mapping a low-dimensional ?p space to a Banach space with an easily computable norm. We use that algorithm to show that Matsaev’s proposed extension of the inequality of John von Neumann is false in case p=4. Matsaev conjectured that for every contraction T on Lp (1<p<∞) one has for any polynomial P
‖P(T)‖Lp→Lp?‖P(S)‖?p(Z+)→?p(Z+) 相似文献
3.
4.
Matthias Neufang 《Journal of Functional Analysis》2005,224(1):217-229
Let A be a Banach algebra, and consider A** equipped with the first Arens product. We establish a general criterion which ensures that A is left strongly Arens irregular, i.e., the first topological centre of A** is reduced to A itself. Using this criterion, we prove that for a very large class of locally compact groups, Ghahramani-Lau's conjecture (cf. [Lau 94] and [Gha-Lau 95]) stating the left strong Arens irregularity of the measure algebra M(G), holds true. (Our methods obviously yield as well the right strong Arens irregularity in the situation considered.)Furthermore, the same condition used above implies that every linear left A**-module homomorphism on A* is automatically bounded and w*-continuous. We finally show that our criterion also yields a partial answer to a question raised by Lau-Ülger (Trans. Amer. Math. Soc. 348 (3) (1996) 1191) on the topological centre of the algebra (A*⊙A)*, for A having a right approximate identity bounded by 1. 相似文献
5.
In this note we determine when topological simplicity of a subsemigroup implies its simplicity. A measure theoretic approach is used. The main result is: In a locally compact completely simple semigroup whose maximal subgroups are compact, every subsemigroup which is either locally compact or of non-empty interior is completely simple. As a corollary, we have: In a compact semigroup, any topologically simple subsemigroup which is either locally compact or of non-empty interior is simple. 相似文献
6.
7.
David E. Evans 《Acta Appl Math》1984,2(3-4):333-352
A survey of the recent work on the infinitesimal generators of one-parameter semigroups of positivity preserving maps on operator algebras, in the presence of compact symmetry groups or flows. 相似文献
8.
9.
Humberto E. Prado 《Acta Appl Math》1991,25(1):87-98
Local transformation groups acting on a manifold X define a natural action of on a space D(X), of functions on X. The natural action induces a local representation of on a Hilbert subspace of the space of distributions on D(X). 相似文献
10.
11.
The C*-algebra
generated by the Bergman and anti-Bergman projections and by the operators of multiplication by piecewise continuous functions on the Lebesgue space L2(Π) over the upper half-plane is studied. Making use of a local principle, limit operators techniques, and the Plamenevsky results on two-dimensional singular integral operators with coefficients admitting homogeneous discontinuities we reduce the study to simpler C*-algebras associated with points
and pairs
We construct a symbol calculus for unital C*-algebras generated by n orthogonal projections sum of which equals the unit and by m one-dimensional orthogonal projections. Such algebras are models of local algebras at points z ∈∂Π being the discontinuity points of coefficients. A symbol calculus for the C*- algebra
and a Fredholm criterion for the operators
are obtained. Finally, a C*-algebra isomorphism between the quotient algebra
where
is the ideal of compact operators, and its analogue
for the unit disk is constructed. 相似文献
12.
Complementing the work of T.-S. Liu and A.C.M. van Rooij we show that the existence of non-zero translation invariant operators between certain function spaces on a locally compact group implies its amenability. 相似文献
13.
Jean Ludwig 《Journal of Functional Analysis》2006,233(1):206-227
We extend the results by Froelich and Spronk and Turowska on the connection between operator synthesis and spectral synthesis for A(G) to second countable locally compact groups G. This gives us another proof that one-point subset of G is a set of spectral synthesis and that any closed subgroup is a set of local spectral synthesis. Furthermore, we show that “non-triangular” sets are strong operator Ditkin sets and we establish a connection between operator Ditkin sets and Ditkin sets. These results are applied to prove that any closed subgroup of G is a local Ditkin set. 相似文献
14.
The congruence extension property (CEP) of semigroups has been extensively studied by a number of authors. We call a compact semigroup S an Ω-compact semigroup if the set of all regular elements of S forms an ideal of S. In this note, we characterize the Ω-compact semigroup having (CEP). Our result extends a recent result obtained by X.J. Guo on the congruence extension property of strong Ω-compact semigroups which is a semigroup containing precisely one regular D-class. 相似文献
15.
Volker Runde 《Monatshefte für Mathematik》1997,123(3):245-252
LetG be a Moore group, letB be a Banach algebra, and let :L
1(G)B be a homomorphism. We show that is continuous if and only if its restriction to the center ofL
1(G) is continuous. As a consequence, we obtain that (i) every homomorphism fromL
1(G) orC
*(G) onto a dense subalgebra of a semisimple Banach algebra, and (ii) every epimorphism fromC
*(G) onto a Banach algebra is automatically continuous. 相似文献
16.
Suppose that G is a locally compact group and π is a (not necessarily irreducible) unitary representation of a closed normal subgroup N of G on a Hilbert space . We extend results of Clifford and Mackey to determine when π extends to a unitary representation of G on the same space in terms of a cohomological obstruction. 相似文献
17.
18.
19.
Natalia Babych Yuri Golovaty 《Journal of Computational and Applied Mathematics》2010,234(6):1860-1867
We study eigenvibrations for inhomogeneous string consisting of two parts with strongly contrasting stiffness and mass density. In this work we treat a critical case for the high frequency approximations, namely the case when the order of mass density inhomogeneity is the same as the order of stiffness inhomogeneity, with heavier part being softer. The limit problem for high frequency approximations depends nonlinearly on the spectral parameter. The quantization of the spectral semiaxis is applied in order to get a close approximations of eigenvalues as well as eigenfunctions for the prime problem under perturbation. 相似文献
20.
Let G be an additive subgroup of a normed space X. We say that a point is weakly separated (resp. -separated) from G if it can be separated from G by a continuous character (resp. by a continuous positive definite function). Let T : X → Y be a continuous linear operator. Consider the following conditions:
(ws) if , then x is weakly separated from G;
(ps) if , then x is -separated from G;
(wp) if Tx is -separated from T(G), then x is weakly separated from G.
By (resp. , ) we denote the class of operators T : X → Y which satisfy (ws) (resp. (ps), (wp)) for all and all subgroups G of X. The paper is an attempt to describe the above classes of operators for various Banach spaces X, Y. It is proved that if X, Y are Hilbert spaces, then is the class of Hilbert-Schmidt operators. It is also shown that if T is a Hilbert-to-Banach space operator with finite ℓ-norm, then .
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