共查询到20条相似文献,搜索用时 15 毫秒
1.
Meng-Kuang Kuo 《Positivity》2009,13(4):745-758
In this paper, we introduce the concept of w-almost convergent sequences. Such a definition is a weak form of almost convergent
sequences given by G. G. Lorentz in [Acta Math. 80(1948),167-190]. We give a detailed study on w-almost convergent double
sequences and prove that w-almost convergence and almost convergence are equivalent under the boundedness of the given sequence.
The Tauberian results for w-almost convergence are established. Our Tauberian results generalize a result of Lorentz and Tauber’s
second theorem. Moreover, we prove that w-almost convergence and norm convergence are equivalent for the sequence of the rectangular
partial sums of the Fourier series of f ∈ Lp(T2), where 1 < p < ∞.
相似文献
2.
We prove that the algebraic dimension of the linear span of sums of a subseries convergent series in a Hausdorff topological linear space is either finite or equals 2°. This result is applied to represent every infinite-dimensional metrizable linear spaee of cardinality 2° as the direct sum of a sequence of dense subspaces with a strange summability property. Moreover, we show that every infinite-dimensional separable metrizable linear space admits an m-quasi-basis which is not a quasi-basis.Some results of this paper were presented at the 9th Winter School on Abstract Analysis in Srni (Czechoslovakia), January 1981 相似文献
3.
Constructive groups were introduced by Sternfeld in [6] as a class of metrizable groupsG for which a suitable version of the Stone-Weierstrass theorem on the group ofG-valued functionsC(X, G) remains valid. As a way of exploring the existence of such Stone-Weierstrass-type theorems in this context we address the
question raised in [6] as to which groups are constructive and prove that a locally compact group with more than two elements
is constructive if and only if it is either totally disconnected or homeomorphic to some vector group ℝ
n
. It may therefore be concluded that the Stone-Weierstrass theorem can be extended to some noncommutative Lie groups — exactly
to those not containing any nontrivial compact subgroup.
Research partially supported by Grant CTIDIB/2002/192 of theAgencia Valenciana de Ciencia y Tecnología, and Fundació Caixa-Castelló, grant P1 B2001-08. 相似文献
4.
We prove that a collection (X, Y, Z) is a Lebesgue triple if X is a metrizable space, Y is a perfectly normal space, and Z is a strongly σ-metrizable topological vector space with stratification (Z
m)
m = 1∞, where, for every m ∈ ℕ, Z
m is a closed, metrizable, separable subspace of Z that is arcwise connected and locally arcwise connected.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 12, pp. 1639–1646, December, 2007. 相似文献
5.
Letf be a continuous function on the unit circle Γ, whose Fourier series is ω-absolutely convergent for some weight ω on the set
of integersZ. If f is nowhere vanishing on Γ, then there exists a weightv onZ such that 1/f hadv-absolutely convergent Fourier series. This includes Wiener’s classical theorem. As a corollary, it follows that if φ is holomorphic
on a neighbourhood of the range off, then there exists a weight Χ on Z such that φ ◯f has Χ-absolutely convergent Fourier series. This is a weighted analogue of Lévy’s generalization of Wiener’s theorem. In
the theorems,v and Χ are non-constant if and only if ω is non-constant. In general, the results fail ifv or Χ is required to be the same weight ω. 相似文献
6.
Gerald Beer 《Monatshefte für Mathematik》2000,129(4):267-280
By a metric mode of convergence to infinity in a regular Hausdorff space X, we mean a sequence of closed subsets of X with and , and a sequence (or net) in X is convergent to infinity with respect to provided for each contains eventually. Modulo a natural equivalence relation, these correspond to one-point extensions of the space with a countable
base at the ideal point, and in the metrizable setting, they correspond to metric boundedness structures for the space. In
this article, we study the interplay between these objects and certain continuous functions that may determine the metric
mode of convergence to infinity, called forcing functions. Falling out of our results is a simple proof that each noncompact
metrizable space admits uncountably many distinct metric uniformities.
(Received 2 March 1999) 相似文献
7.
T. Deck 《Potential Analysis》2006,24(1):63-86
This work investigates complex random fields Z, which have a rotation invariant path measure. Fields of this type are constructed and analyzed in terms of (pathwise convergent)
L2-expansions, and quasi invariance properties of their path measures are studied. The results are used to investigate ℋL2(Z), the space of holomorphic L2-functionals of Z. Conditions are given such that every F∈ℋL2(Z) admits an L2-power series expansion, and a general skeleton theorem is proved, which justifies the notion ‘holomorphic’.
Mathematics Subject Classifications (2000) 60G07, 60G30, 60G60.
T. Deck: Financial support from FCP, Portugal, is gratefully acknowledged. 相似文献
8.
M. Khazaradze 《Georgian Mathematical Journal》1996,3(2):121-132
The theorem on the tending to zero of coefficients of a trigonometric series is proved when theL
1-norms of partial sums of this series are bounded. It is shown that the analog of Helson's theorem does not hold for orthogonal series with respect to the bounded orthonormal system. Two facts are given that are similar to Weis' theorem on the existence of a trigonometric series which is not a Fourier series and whoseL
1-norms of partial sums are bounded. 相似文献
9.
Gerald Beer 《Monatshefte für Mathematik》2000,7(3):267-280
By a metric mode of convergence to infinity in a regular Hausdorff space X, we mean a sequence of closed subsets of X with and , and a sequence (or net) in X is convergent to infinity with respect to provided for each contains eventually. Modulo a natural equivalence relation, these correspond to one-point extensions of the space with a countable base at the ideal point, and in the metrizable setting, they correspond to metric boundedness structures for the space. In this article, we study the interplay between these objects and certain continuous functions that may determine the metric mode of convergence to infinity, called forcing functions. Falling out of our results is a simple proof that each noncompact metrizable space admits uncountably many distinct metric uniformities. 相似文献
10.
W. J. Stiles 《Israel Journal of Mathematics》1970,8(1):53-56
In this note, we show that a series, Σx
n
, in a complete linear metric space with a basis is subseries convergent if and only if it is weakly subseries convergent. 相似文献
11.
Necessary and sufficient conditions are found for the almost sure convergence of almost all simple rearrangements of a series
of Banach space valued random variables. The results go back to Nikishin’s well-known theorem on the existence of an almost
surely convergent rearrangement of a numerical random series. An example is also given of a numerical random series with general
term tending to zero almost surely such that this series converges in probability and any its rearrangement diverges almost
surely. 相似文献
12.
Let K be a Hausdorff space and C
b
(K) be the Banach algebra of all complex bounded continuous functions on K. We study the Gateaux and Fréchet differentiability of subspaces of C
b
(K). Using this, we show that the set of all strong peak functions in a nontrivial separating separable subspace H of C
b
(K) is a dense G
δ subset of H, if K is compact. This gives a generalized Bishop’s theorem, which says that the closure of the set of all strong peak points for
H is the smallest closed norming subset of H. The classical Bishop’s theorem was proved for a separating subalgebra H and a metrizable compact space K. 相似文献
13.
For functions which are Henstock–Kurzweil integrable but not Lebesgue-integrable we prove a theorem which resembles the Riemann theorem on the rearrangement of conditionally convergent series.
相似文献14.
The main aim of this paper is to prove that the logarithmic means of quadratical partial sums of the double Walsh-Fourier series does not improve the convergence in measure. In other words, we prove that for any Orlicz space, which is not a subspace of LlnL(I2), the set of the functions having logarithmic means of quadratical partial sums of the double Walsh-Fourier series convergent in measure is of first Baire category. 相似文献
15.
J. M. Calabuig F. Galaz-Fontes E. Jiménez-Fernández E. A. Sánchez Pérez 《Mathematische Zeitschrift》2007,257(2):381-402
In this paper, we characterize the space of multiplication operators from an L
p
-space into a space L
1(m) of integrable functions with respect to a vector measure m, as the subspace defined by the functions that have finite p-semivariation. We prove several results concerning the Banach lattice structure of such spaces. We obtain positive results—for
instance, they are always complete, and we provide counterexamples to prove that other properties are not satisfied—for example,
simple functions are not in general dense. We study the operators that factorize through , and we prove an optimal domain theorem for such operators. We use our characterization to generalize the Bennet–Maurey–Nahoum
Theorem on decomposition of functions that define an unconditionally convergent series in L
1[0,1] to the case of 2-concave Banach function spaces.
The research was partially supported by Proyecto MTM2005-08350-c03-03 and MTN2004-21420-E (J. M. Calabuig). Proyecto CONACyT
42227 (F. Galaz-Fontes). Proyecto MTM2006-11690-c02-01 and Feder (E. Jiménez-Fernández and E. A. Sánchez Pérez). 相似文献
16.
Theorem 1. LetX be a Banach space. (a) IfX
∗ has a closed subspace in which no normalized sequence converges weak∗ to zero, thenl
1 is isomorphic to a subspace ofX. (b) IfX
∗ contains a bounded sequence which has no weak∗ convergent subsequence, thenX contains a separable subspace whose dual is not separable.
The second-named author was supported in part by NSF-MPS 72-04634-A03. 相似文献
17.
We use interpolation methods to prove a new version of the limiting case of the Sobolev embedding theorem, which includes
the result of Hansson and Brezis-Wainger for W
n
k/k
as a special case. We deal with generalized Sobolev spaces W
A
k
, where instead of requiring the functions and their derivatives to be in Ln/k, they are required to be in a rearrangement invariant space A which belongs to a certain class of spaces “close” to Ln/k.
We also show that the embeddings given by our theorem are optimal, i.e., the target spaces into which the above Sobolev spaces
are shown to embed cannot be replaced by smaller rearrangement invariant spaces. This slightly sharpens and generalizes an,
earlier optimality result obtained by Hansson with respect to the Riesz potential operator.
In memory of Gene Fabes.
Acknowledgements and Notes This research was supported by Technion V.P.R. Fund-M. and C. Papo Research Fund. 相似文献
18.
For 0<p<∞, let Hp(R
n) denote the Lebesgue space for p>1 and the Hardy space for p ≤1. In this paper, the authors study Hp(R
n)×Hq(R
n)→Hr(R
n) mapping properties of bilinear operators given by finite sums of the products of the standard fractional integrals or the
standard fractional integral with the Calderón-Zygmund operator. The authors prove that such mapping properties hold if and
only if these operators satisfy certain cancellation conditions.
Supported by the NNSF and the National Education Comittee of China. 相似文献
19.
A bounded linear operator between Banach spaces is calledcompletely continuous if it carries weakly convergent sequences into norm convergent sequences. Isolated is a universal operator for the class
of non-completely-continuous operators fromL
1 into an arbitrary Banach space, namely, the operator fromL
1 into ⊆∞ defined byT
0(f) = (∫r
n
f
d
μ)
n>-0, wherer
n
is thenth Rademacher function. It is also shown that there does not exist a universal operator for the class of non-completely-continuous
operators between two arbitrary Banach spaces. The proof uses the factorization theorem for weakly compact operators and a
Tsirelson-like space.
Supported in part by NSF grant DMS-9306460. Participant, NSF Workshop in Linear Analysis & Probability, Texas A&M University
(supported in part by NSF grant DMS-9311902).
Supported in part by NSF grant DMS-9003550. 相似文献
20.
Mourad Oudghiri 《Integral Equations and Operator Theory》2005,53(4):535-545
In the present paper we examine the stability of Weyl’s theorem under perturbations. We show that if T is an isoloid operator on a Banach space, that satisfies Weyl’s theorem, and F is a bounded operator that commutes with T and for which there exists a positive integer n such that Fn is finite rank, then T + F obeys Weyl’s theorem. Further, we establish that if T is finite-isoloid, then Weyl’s theorem is transmitted from T to T + R, for every Riesz operator R commuting with T. Also, we consider an important class of operators that satisfy Weyl’s theorem, and we give a more general perturbation results
for this class. 相似文献