共查询到20条相似文献,搜索用时 15 毫秒
1.
We obtain a new closed graph theorem which is a substantial improvement of a recent result. 相似文献
2.
Chunjie Wang 《Integral Equations and Operator Theory》2007,58(4):597-601
We prove a stability theorem for the nullity of a linear combination c
1
P
1 + c
2
P
2 of two idempotent operators P
1, P
2 on a Banach space provided c
1, c
2 and c
1 + c
2 are nonzero. We then show that for c
1
P
1 + c
2
P
2 the property of being upper semi-Fredholm, lower semi-Fredholm and Fredholm, respectively, is independent of the choice of
c
1, c
2, and that the nullity, defect and index of c
1
P
1 + c
2
P
2 are stable. 相似文献
3.
This paper mainly concerns the essential normality of graded submodules. Essentially all of the basic Hilbert modules that
have received attention over the years are p-essentially normal—including the d-shift Hilbert module, the Hardy and Bergman modules of the unit ball. Arveson conjectured graded submodules over the unit
ball inherit this property and provided motivations to seek an affirmative answer. Some positive results have been obtained
by Arveson and Douglas. However, the problem has been resistant. In dimensions d = 2, 3, this paper shows that the Arveson’s conjecture is true. In any dimension, the paper also gives an affirmative answer
in the case of the graded principal submodule. Finally, the paper is associated with K-homology invariants arising from graded quotient modules, by which geometry of the quotient modules and geometry of algebraic
varieties are connected. In dimensions d = 2, 3, it is shown that K-homology invariants determined by graded quotients are nontrivial. The paper also establishes results on p-smoothness of K-homology elements, and gives an explicit expression for K-homology invariant in dimension d = 2. 相似文献
4.
This paper mainly considers Toeplitz algebras, subnormal tuples and rigidity concerning reproducing C[z1,…,zd]-modules. By making use of Arveson's boundary representation theory, we find there is more rigidity in several variables than there is in single variable. We specialize our attention to reproducing C[z1,…,zd]-modules with -invariant kernels by examining the spectrum and the essential spectrum of the d-tuple {Mz1,…,Mzd}, and deducing an exact sequence of C∗-algebras associated with Toeplitz algebra. Finally, we deal with Toeplitz algebras defined on Arveson submodules and rigidity of Arveson submodules. 相似文献
5.
Kunyu Guo 《Journal of Functional Analysis》2004,213(2):380-411
This paper mainly concerns defect operators and defect functions of Hardy submodules, Bergman submodules over the unit ball, and Hardy submodules over the polydisk. The defect operator (function) carries key information about operator theory (function theory) and structure of analytic submodules. The problem when a submodule has finite defect is attacked for both Hardy submodules and Bergman submodules. Our interest will be in submodules generated by polynomials. The reason for choosing such submodules is to understand the interaction of operator theory, function theory and algebraic geometry. 相似文献
6.
Yongjiang Duan 《Integral Equations and Operator Theory》2007,58(3):301-314
This paper is to study the quasihomogeneous Hilbert modules and generalize a result of Arveson [3] which relates the curvature
invariant to the index of the Dirac operator.
This work was partially supported by NKBRPC (#2006CB805905) and SRFDP. 相似文献
7.
Sandor Z. Németh 《Positivity》2007,11(3):469-475
The isotone projection cone, defined by G. Isac and A. B. Németh, is a closed pointed convex cone such that the order relation
defined by the cone is preserved by the projection operator onto the cone. In this paper the coisotone cone will be defined
as the polar of a generating isotone projection cone. Several equivalent inequality conditions for the coisotonicity of a
cone in Euclidean spaces will be given.
Thanks are due to A. B. Németh who draw the author’s attention on the relation of latticial cones generated by vectors with
pairwise non-accute angles with the theory of isotone cones. 相似文献
8.
《Quaestiones Mathematicae》2013,36(8):1117-1133
AbstractPrior to investigating on sequence spaces and their convergence, we study the notion of statistical convergence of difference sequences of fractional order α ∈ ?. As generalizations of previous works, this study includes several special cases under different limiting conditions of α, such as the notion of statistical convergence of difference sequences of zeroth and mth (integer) order. In fact, we study certain new results on statistical convergence via the difference operator Δα and interpret them to those of previous works. Also, by using the convergence of Δα-summable sequences which is stronger than statistical convergence of difference sequences, we apply classical Bernstein operator and a generalized form of Meyer-Konig and Zeller operator to construct an example in support of our result. Also, we study the rates of Δα-statistical convergence of positive linear operators. 相似文献
9.
51.IntroductionandPreliminariesThroughoutthispaper(X,11'if)denotesanormedspaceandN(11'II)denotesthecollectionofallnormsonXwhichareequivalentto11'11.Foreach11'if'6N(II'II)andeachr>0,letX.(ll'II')~{xEX:Ilxll'5r}andX?(ll'if')~{xEX.Ilxll'相似文献
10.
We give several unifying results, interpretations, and examples regarding the convergence of the von Neumann alternating projection algorithm for two arbitrary closed convex nonempty subsets of a Hilbert space. Our research is formulated within the framework of Fejér monotonicity, convex and set-valued analysis. We also discuss the case of finitely many sets. 相似文献
11.
Z. D. Arova 《Integral Equations and Operator Theory》1997,28(1):1-16
The known model of aj-unitary node with a givenj-inner characteristic matrix functionW is obtained from the known model of a unitary node with a given bi-inner characteristic matrix functionS, using the Potapov-Ginzburg transforms of the nodes and their characteristic functionsW andS. We show that some new properties of the L. de Branges reproducing kernal Hilbert spaces
(W) which were discovered by H. Dym are characteristic properties of these spaces. 相似文献
12.
13.
Fernanda Botelho 《Linear algebra and its applications》2010,432(1):275-282
We characterize essential normality for certain elementary operators acting on the Hilbert-Schmidt class. We find the Aluthge transform of an elementary operator of length one. We show that the Aluthge transform of an elementary 2-isometry need not be a 2-isometry. We also characterize hermitian elementary operators of length 2. 相似文献
14.
15.
We continue the study of a generalization of L. de Branges's theory of Hilbert spaces of entire functions to the Pontryagin space setting. In this-second-part we investigate isometric embeddings of spaces of entire functions into spacesL
2 () understood in a distributional sense and consider Weyl coefficients of matrix chains. The main task is to give a proof of an indefinite version of the inverse spectral theorem for Nevanlinna functions. Our methods use the theory developed by L. de Branges and the theory of extensions of symmetric operators of M.G.Krein. 相似文献
16.
Let K1,…,Kn be (infinite) non-negative matrices that define operators on a Banach sequence space. Given a function f:[0,∞)×…×[0,∞)→[0,∞) of n variables, we define a non-negative matrix and consider the inequality
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