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1.
B. Nagy 《Proceedings of the American Mathematical Society》1998,126(5):1433-1444
Spectral operators of scalar type in the sense of Dunford often occur in connection with unconditionally convergent series expansions, whereas conditionally convergent expansions under similar conditions may be described with the help of operators having a more general type of spectral decomposition. We show that under certain conditions even in the latter case we can restrict our considerations to a dense linear submanifold of the original Banach space with a stronger topology, where the convergence of the expansion under study will be unconditional. Though our conditions could be formulated in terms of a single operator, it seems to be more natural to state them in terms of (the generator of) a periodic group of operators.
2.
讨论Banach空间中算子级数的无条件收敛.分别在自反和含无条件基的条件下推广了Vcctor和Cary关于Hilbert空间的两个相应结果.即[1]的定理2和命题6.并且肯定回答了他们留下的问题. 相似文献
3.
We prove that some results on uniform convergence of sequences of unconditionally convergent series, in Banach spaces, can
be generalized to sequences of weakly unconditionally Cauchy series.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
4.
In this paper we obtain new characterizations of weakly unconditionally Cauchy series and unconditionally convergent series through Cesàro summability. We study new spaces associated to a series in a Banach space; as a consequence, new characterizations of complete and barrelled normed spaces are proved. 相似文献
5.
We introduce the class of Orlicz-Pettis polynomials between Banach spaces, defined by their action on weakly unconditionally
Cauchy series. We give a number of equivalent definitions, examples and counterexamples which highlight the differences between
these polynomials and the corresponding linear operators. 相似文献
6.
Ivan Singer 《Israel Journal of Mathematics》1964,2(4):249-250
We give a new proof of the famous Dvoretzky-Rogers theorem ([2], Theorem 1), according to which a Banach spaceE is finite-dimensional if every unconditionally convergent series inE is absolutely convergent. 相似文献
7.
We introduce the class of Orlicz-Pettis polynomials between Banach spaces, defined by their action on weakly unconditionally
Cauchy series. We give a number of equivalent definitions, examples and counterexamples which highlight the differences between
these polynomials and the corresponding linear operators.
(Received 17 May 1999; in revised form 6 October 1999) 相似文献
8.
We show that for each Banach ideal of homogeneous polynomials, there exists a (necessarily unique) Banach operator ideal compatible with it. Analogously, we prove that any ideal of n-homogeneous polynomials belongs to a coherent sequence of ideals of k-homogeneous polynomials. 相似文献
9.
We show that for each Banach ideal of homogeneous polynomials, there exists a (necessarily unique) Banach operator ideal compatible
with it. Analogously, we prove that any ideal of n-homogeneous polynomials belongs to a coherent sequence of ideals of k-homogeneous polynomials. 相似文献
10.
We derive Banach-Stone theorems for spaces of homogeneous polynomials. We show that every isometric isomorphism between the spaces of homogeneous approximable polynomials on real Banach spaces E and F is induced by an isometric isomorphism of E′ onto F′. With an additional geometric condition we obtain the analogous result in the complex case. Isometries between spaces of homogeneous integral polynomials and between the spaces of all n-homogeneous polynomials are also investigated. 相似文献
11.
Erhan Çalişkan 《Czechoslovak Mathematical Journal》2007,57(2):763-776
We show that a Banach space E has the weakly compact approximation property if and only if each continuous Banach-valued polynomial on E can be uniformly approximated on compact sets by homogeneous polynomials which are members of the ideal of homogeneous polynomials
generated by weakly compact linear operators. An analogous result is established also for the compact approximation property. 相似文献
12.
13.
Leonardo Pellegrini 《Journal of Mathematical Analysis and Applications》2007,332(1):272-278
In this work we present some conditions of equivalence for the existence of a monomial basis in spaces of homogeneous polynomials on Banach spaces. 相似文献
14.
We show that the centraliser of the space of n-fold symmetric injective tensors, n≥2, on a real Banach space is trivial. With a geometric condition on the set of extreme points of its dual, the space of integral
polynomials we obtain the same result for complex Banach spaces. We give some applications of this results to centralisers
of spaces of homogeneous polynomials and complex Banach spaces. In addition, we derive a Banach-Stone Theorem for spaces of
vector-valued approximable polynomials.
This project was supported in part by Enterprise Ireland, International Collaboration Grant – 2004 (IC/2004/009). The second
author was also partially supported by PIP 5272,UBACYTX108 and PICT 03-15033 相似文献
15.
Daniel Alpay Flor de María Correa-Romero María Elena Luna-Elizarrarás Michael Shapiro 《Integral Equations and Operator Theory》2011,71(3):311-326
The Fueter variables form a basis of the space of (quaternionic or Cliffordian) hyperholomorphic homogeneous polynomials of
degree one, and their symmetrized products give the respective bases of spaces of hyperholomorphic homogeneous polynomials
for any degree k. In the present paper we introduce new bases, i.e., new types of hyperholomorphic variables which lead to the Taylor-type
series expansions reflecting the structure of the set of all (quaternionic or Cliffordian algebra-valued) hyperholomorphic
functions. 相似文献
16.
This paper is the first systematic study of homogeneous polynomials on Banach lattices. A variety of new Banach spaces and Banach lattices of multilinear maps, homogeneous polynomials, and operators are introduced. The main technique is to employ positive tensor products and quotients of positive tensor products. Our theorems generalize the results on orthogonally additive polynomials by Benyamini, Lassalle, and Llavona (2006) in [4], the results by Grecu and Ryan (2005) in [14], and the results by Sundaresan (1991) in [23]. 相似文献
17.
Z. A. Kusraeva 《Siberian Mathematical Journal》2016,57(3):519-524
We prove an analog of the Dodds–Fremlin–Wickstead Theorem on compact domination for homogeneous orthogonally additive polynomials in Banach lattices. The proof is based on linearization of the polynomials which was established earlier by the author. 相似文献
18.
We consider different kinds of convergence of homogeneous polynomials and multilinear forms in random variables. We show that for a variety of complex random variables, the almost sure convergence of the polynomial is equivalent to that of the multilinear form, and to the square summability of the coefficients. Also, we present polynomial Khintchine inequalities for complex gaussian and Steinhaus variables. All these results have no analogues in the real case. Moreover, we study the Lp-convergence of random polynomials and derive certain decoupling inequalities without the usual tetrahedral hypothesis. We also consider convergence on “full subspaces” in the sense of Sjögren, both for real and complex random variables, and relate it to domination properties of the polynomial or the multilinear form, establishing a link with the theory of homogeneous polynomials on Banach spaces. 相似文献
19.
本文首先给出复Banach空间单位球上一类α次星形映射齐次展开式各项的精细估计,特别当这些映射又是k折对称映射时,估计还是精确的.其次建立C~n中单位多圆柱上上述推广映射齐次展开式各项的精细估计,同样当这些映射又是k折对称映射时,估计仍是精确的.由此证明了多复变数中关于α次星形映射的弱Bieberbach猜想,且所得到的估计都能回到单复变数的情形. 相似文献
20.
Benyamini Yoav; Lassalle Silvia; Llavona Jose G. 《Bulletin London Mathematical Society》2006,38(3):459-469
The main result in this paper is a representation theorem forhomogeneous orthogonally additive polynomials on Banach lattices.The representation theorem is used to study the linear spanof the set of zeros of homogeneous real-valued orthogonallyadditive polynomials. It is shown that in certain lattices everyelement can be represented as the sum of two or three zerosor, at least, can be approximated by such sums. It is also indicatedhow these results can be used to study weak topologies inducedby orthogonally additive polynomials on Banach lattices. 2000Mathematics Subject Classification 46G25, 46B42, 47B38. 相似文献