共查询到20条相似文献,搜索用时 15 毫秒
1.
E.S. Belinskii E.R. Liflyand R.M. Trigub 《Journal of Fourier Analysis and Applications》1996,3(2):103-129
Beurling's algebra $A^*=\{f:\sum_{k=0}^{\infty} \sup_{k\le |m|} |\hat f (m)| < \infty \}Beurling’s algebra $A^* = \{ f:\sum\nolimits_{k = 0}^\infty {\sup _{k \leqslant |m|} |\hat f(m)|< \infty } \} $ is considered. A* arises quite naturally in problems of summability of the Fourier series at Lebesgue points, whereas Wiener’s algebra A of functions with absolutely convergent Fourier series arises when studying the norm convergence of linear means. Certainly, both algebras are used in some other areas. A* has many properties similar to those of A, but there are certain essential distinctions. A* is a regular Banach algebra, its space of maximal ideals coincides with[?π, π], and its dual space is indicated. Analogs of Herz’s and Wiener-Ditkin’s theorems hold. Quantitative parameters in an analog of the Beurling-Pollard theorem differ from those for A. Several inclusion results comparing the algebra A* with certain Banach spaces of smooth functions are given. Some special properties of the analogous space for Fourier transforms on the real axis are presented. The paper ends with a summary of some open problems. 相似文献
2.
Algebra matrix and similarity classification of operators 总被引:1,自引:0,他引:1
ZHANG Zilong & LI Yucheng Department of Mathematics Hebei Normal University Shijiazhuang China 《中国科学A辑(英文版)》2006,49(3):398-409
In this paper, by the Gelfand representation theory and the Silov idempotents theorem, we first obtain a central decomposition theorem related to a unital semi-simple n-homogeneous Banach algebra, and then give a similarity classification of two strongly irreducible Cowen-Douglas operators using this theorem. 相似文献
3.
4.
Christoph Klein 《manuscripta mathematica》1986,55(3-4):403-418
We recall that the n-valued Riemann integrable functions resp. more general: the Banach space (algebra) -valued Darboux integrable functions — on the compact support of a non negative Radon measure are a Banach space (algebra) with respect to the ess. sup. norm. It is shown that the Darboux integrable functions with a precompact range also form a Banach space (algebra). For this space we deduce a direct analogue of Arzela-Ascoli's theorem. 相似文献
5.
We study some properties of the algebras of continuous functions on a locally compact space whose topology is defined by the family of all multiplication operators (β-uniform algebras). We introduce the notion of a β-amenable algebra and show that a β-uniform algebra is β-amenable if and only if it coincides with the algebra of bounded functions on a locally compact space (an analog of M. V. She?nberg’s theorem for uniform algebras). 相似文献
6.
A synaptic algebra is an abstract version of the partially ordered Jordan algebra of all bounded Hermitian operators on a
Hilbert space. We review the basic features of a synaptic algebra and then focus on the interaction between a synaptic algebra
and its orthomodular lattice of projections. Each element in a synaptic algebra determines and is determined by a one-parameter
family of projections—its spectral resolution. We observe that a synaptic algebra is commutative if and only if its projection
lattice is boolean, and we prove that any commutative synaptic algebra is isomorphic to a subalgebra of the Banach algebra
of all continuous functions on the Stone space of its boolean algebra of projections. We study the so-called range-closed
elements of a synaptic algebra, prove that (von Neumann) regular elements are range-closed, relate certain range-closed elements
to modular pairs of projections, show that the projections in a synaptic algebra form an M-symmetric orthomodular lattice,
and give several sufficient conditions for modularity of the projection lattice. 相似文献
7.
Let VR denote the Banach algebra of absolutely continuous functionsof bounded total variation on R, and let Bp be the Banach algebraof bounded linear operators acting on the Lebesgue space LpRfor 1 < p < . We study the Banach algebra A Bp generatedby the pseudodifferential operators of zero order with slowlyoscillating VR-valued symbols on R. Boundedness and compactnessconditions for pseudodifferential operators with symbols inL R, VR are obtained. A symbol calculus for the non-closed algebraof pseudodifferential operators with slowly oscillating VR-valuedsymbols is constructed on the basis of an appropriate approximationof symbols by infinitely differentiable ones and by use of thetechniques of oscillatory integrals. As a result, the quotientBanach algebra A = A K, where K is the ideal of compact operatorsin Bp, is commutative and involutive. An isomorphism betweenthe quotient Banach algebra A of pseudodifferential operatorsand the Banach algebra of their Fredholm symbols is established. A Fredholm criterionand an index formula for the pseudodifferential operators A A are obtained in terms of their Fredholm symbols. 2000 MathematicsSubject Classification 47G30, 47L15 (primary), 47A53, 47G10(secondary). 相似文献
8.
H. Rezaei 《Complex Analysis and Operator Theory》2013,7(6):1877-1887
Let $\mathcal A $ be a semigroup of bounded linear operators on the Banach algebra $B(X)$ for a separable Banach space $X$ . We show the transitivity of $\mathcal A $ with the operator norm topology, implies hypercyclicity with the strong operator topology (SOT) while the converse may not be true. As a consequence, SOT-transitive semigroup of left multiplication operators on $B(X)$ is characterized. 相似文献
9.
E. S. Belinskii E. R. Liflyand R. M. Trigub 《Journal of Fourier Analysis and Applications》1997,3(2):103-129
Beurling’s algebra
is considered. A* arises quite naturally in problems of summability of the Fourier series at Lebesgue points, whereas Wiener’s
algebra A of functions with absolutely convergent Fourier series arises when studying the norm convergence of linear means.
Certainly, both algebras are used in some other areas. A* has many properties similar to those of A, but there are certain
essential distinctions. A* is a regular Banach algebra, its space of maximal ideals coincides with[−π, π], and its dual space is indicated. Analogs of Herz’s and Wiener-Ditkin’s theorems hold. Quantitative parameters in an analog
of the Beurling-Pollard theorem differ from those for A. Several inclusion results comparing the algebra A* with certain Banach
spaces of smooth functions are given. Some special properties of the analogous space for Fourier transforms on the real axis
are presented. The paper ends with a summary of some open problems. 相似文献
10.
In this paper we study the Banach algebra of singular integral operators with piecewise continuous coefficients and a Carleman orientation-reversing slowly oscillating shift on the Lebesgue space with a power weight on the unit circle. The slow oscillation of the shift derivative, in contrast to the classic assumption on its piecewise continuity, leads to the appearance of massive local spectra for the considered operators. Applying localization techniques and the theory of Mellin pseudodifferential and associated limit operators, we construct a symbol calculus for the above-mentioned operator algebra and find a Fredholm criterion and an index formula for the operators in this algebra in terms of their symbols.Partially supported by CONaCYT grant, Cátedra Patrimonial, No. 990017-EX and by CONACYT project 32726-E, México.Partially supported by F. C. T. grant Praxis XXI/2/2.1/MAT/441/94, Portugal. 相似文献
11.
In this paper, we study the Banach algebra
generated by multidimensional pair integral operators with homogeneous kernels. We describe necessary and sufficient conditions for operators from the algebra
to be Fredholm and present a formula for calculating the index. 相似文献
12.
We construct a convolution algebra of admissible homomorphisms defined on a ‘test space’ to demonstrate the fundamental role of convolution in the study of intertwined evolution operators of linear ordinary differential equations in Banach spaces and probability theory. The choice of test space makes the framework we present quite versatile. The applications include semigroups of linear operators, empathy, integrated semigroups and empathies and the convolution semigroups of probability theory. 相似文献
13.
In this paper, we give an important generalization of Lakshmikantham’s theorem (Theorem 2.1 in Nonlinear Anal Theory Methods Appl 3448–3458, 2009). Our main result asserts the existence of fixed point for a class of nonlinear operators defined in an ordered Banach space, and gives a new monotone Newton-like method to compute this fixed point. We also apply our new result to some important matrix equations. 相似文献
14.
Vyacheslav V. Chistyakov 《Monatshefte für Mathematik》2002,26(5):99-114
We show that the Hardy space of functions of two variables with finite total variation is a Banach algebra under the pointwise
operations and a suitably chosen norm. Then we characterize Nemytskii superposition operators, which map the Hardy space into
itself and satisfy the global Lipschitz condition. 相似文献
15.
范洪福 《应用泛函分析学报》2006,8(4):304-307
讨论向量值函数的Banach代数L∞(T;X)的极大理想空间的拓扑性质和代数性质,得到了若干结果;给出了Banach空间H∞(D;X)中闭单位球的端点的一条性质. 相似文献
16.
Marat Pliev 《Positivity》2017,21(1):23-33
The “Up-and-down” theorem which describes the structure of the Boolean algebra of fragments of a linear positive operator is the well known result in operator theory. We prove an analog of this theorem for a positive abstract Uryson operator defined on a vector lattice and taking values in a Dedekind complete vector lattice. This result is used to prove a theorem of domination for order narrow positive abstract Uryson operators from a vector lattice E to a Banach lattice F with an order continuous norm. 相似文献
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18.
Fredholm perturbation theory and some essential spectra in Banach algebra with respect to subalgebra
《Indagationes Mathematicae》2017,28(2):276-286
The aim of this paper is to enlarge some known results from Fredholm and perturbation theory in the Banach algebra of bounded operators on a Banach space to the Fredholm theory in Banach algebra with respect to a subalgebra. The obtained results allow us to characterize the stability of some essential spectra with respect to a subalgebra. 相似文献
19.
O. N. Masina 《Differential Equations》2008,44(6):872-875
We consider differential inclusions corresponding to accretive operators in a Banach space X for the case in which X is the one-dimensional Euclidean space. We prove existence theorems and an asymptotic stability theorem. We also introduce the notion of a generalizednonincreasing (nondecreasing) multivalued function and establish a relationship between nondecreasing multivalued functions and accretive operators in the one-dimensional Euclidean space. 相似文献
20.
This paper addresses properties of maps of bounded p-variation (p>1) in the sense of N. Wiener, which are defined on a subset of the real line and take values in metric or normed spaces. We prove the structural theorem for these maps and study their continuity properties. We obtain the existence of a Hölder continuous path of minimal p-variation between two points and establish the compactness theorem relative to the p-variation, which is an analog of the well-known Helly selection principle in the theory of functions of bounded variation. We prove that the space of maps of bounded p-variation with values in a Banach space is also a Banach space. We give an example of a Hölder continuous of exponent 0<<1 set-valued map with no continuous selection. In the case p=1 we show that a compact absolutely continuous set-valued map from the compact interval into subsets of a Banach space admits an absolutely continuous selection. 相似文献