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1.
本文利用随机内积空间方法给出了完备赋准范空间上一类无界线性随机算子的谱分解定理。此结果不仅推广了对称随机线性算子的谱分解定理,而且限于原情形也使其处理简明、清晰。 相似文献
2.
Patrick N. Dowling Zhibao Hu Douglas Mupasiri 《Transactions of the American Mathematical Society》1996,348(1):127-139
Complex geometric properties of continuously quasi-normed
spaces are introduced and their relationship to their analogues in real Banach spaces is discussed. It is shown that these properties lift from a continuously quasi-normed space to , for . Local versions of these properties and results are also considered.
spaces are introduced and their relationship to their analogues in real Banach spaces is discussed. It is shown that these properties lift from a continuously quasi-normed space to , for . Local versions of these properties and results are also considered.
3.
U. Luther 《Annali di Matematica Pura ed Applicata》2003,182(2):161-200
We show that the representation theorem for classical approximation spaces can be generalized to spaces A(X,l
q
(ℬ))={f∈X:{E
n
(f)}∈l
q
(ℬ)} in which the weighted l
q
-space l
q
(ℬ) can be (more or less) arbitrary. We use this theorem to show that generalized approximation spaces can be viewed as real
interpolation spaces (defined with K-functionals or main-part K-functionals) between couples of quasi-normed spaces which satisfy certain Jackson and Bernstein-type inequalities. Especially,
interpolation between an approximation space and the underlying quasi-normed space leads again to an approximation space.
Together with a general reiteration theorem, which we also prove in the present paper, we obtain formulas for interpolation
of two generalized approximation spaces.
Received: December 6, 2001; in final form: April 2, 2002?Published online: March 14, 2003 相似文献
4.
It is shown that for every quasi-normed ideal ${\cal Q}$ of
n-homogeneous continuous polynomials between
Banach spaces there is a quasi-normed ideal ${\cal A}$ of
n-linear continuous mappings ${\cal A}$ such that
$q \in {\cal Q}$ if and only if the associated n-linear
mapping $\check{q}$ of q is in ${\cal A}$.
Received: 12 March 2001 相似文献
5.
Oscar Valero 《Proceedings Mathematical Sciences》2008,118(2):245-254
A quasi-normed cone is a pair (X, p) such that X is a (not necessarily cancellative) cone and q is a quasi-norm on X. The aim of this paper is to prove a closed graph and an open mapping type theorem for quasi-normed cones. This is done with
the help of appropriate notions of completeness, continuity and openness that arise in a natural way from the setting of bitopological
spaces. 相似文献
6.
Using the duality theory of sequence spaces, we study in this paper λ-compact operators defined on Banach spaces, corresponding to a sequence space λ. We show that these operators form a quasi-normed operator ideal under suitable restrictions on λ. We also study the relationships of these operators with λ-summing, λ-nuclear and quasi-λ-nuclear operators. The results of this paper generalize the earlier results proved by Sinha and Karn; and also Delgado, Piñeiro and Serrano. 相似文献
7.
A Hahn-Banach type theorem in the frame of quasi-normed spaces (a class of linear spaces with a quasi-uniform structure that contains all linear lattices) is given. The classical result for positive functionals follows as a particular case. 相似文献
8.
We show that the set of semi-Lipschitz functions, defined on a quasi-metric space (X, d), that vanish at a fixed point x0X can be endowed with the structure of a quasi-normed semilinear space. This provides an appropriate setting in which to characterize both the points of best approximation and the semi-Chebyshev subsets of quasi-metric spaces. We also show that this space is bicomplete. 相似文献
9.
We examine for the first time the strong derivative on quasi-normed linear spaces. We show for a large class of such spaces
(including Lp[0,1), 0<p<1, and the block spaces Bq, q≥1) that a Walsh series which converges fast enough is term by term strongly differentiable. We also investigate the case
of term by term pointwise dyadic differentiation on the interval[0,1).
This research supported in part by a National Science Foundation grant INT-8620153 相似文献
10.
11.
By using Aoki-Rolewicz Theorem on p-normalizing a quasi-normed space, we prove stability results for Euler-Lagrange quadratic functional equations in quasi-Banach spaces. These results improve stability results and give the answer to Kim-Rassias's question. 相似文献
12.
A multilinear version of the Boyd interpolation theorem is proved in the context of quasi-normed rearrangement-invariant
spaces. A multilinear Marcinkiewicz interpolation theorem is obtained as a corollary. Several applications are given, including
estimates for bilinear fractional integrals.
Received January 31, 1999 / Accepted February 27, 2000 / Published online December 8, 2000 相似文献
13.
Let (X, d) be a quasi-metric space and (Y, q) be a quasi-normed linear space. We show that the normed cone of semi-Lipschitz functions from (X, d) to (Y, q) that vanish at a point x
0 ∈ X, is balanced. Moreover, it is complete in the sense of D. Doitchinov whenever (Y, q) is a biBanach space.
The authors acknowledge the support of Plan Nacional I+D+I and FEDER, under grant MTM2006-14925-C02-01. The second listed
author is also supported by a grant FPI from the Spanish Ministry of Education and Science. 相似文献
14.
《Journal of Functional Analysis》2023,284(1):109739
We give a sufficient (and, in the case of a compact domain, a necessary) condition for the embedding of Sobolev space of functions with integrable gradient into Besov-Orlicz spaces to be bounded. The condition has a form of a simple integral inequality involving Young and weight functions. We provide an example with Matuszewska-Orlicz indices of involved Orlicz norm equal to one. The main tool is the molecular decomposition of functions from a BV space. 相似文献
15.
16.
Kyriakos Keremedis Eleftherios Tachtsis 《Proceedings of the American Mathematical Society》2007,135(4):1205-1211
We show that the existence of a countable, first countable, zero-dimensional, compact Hausdorff space which is not second countable, hence not metrizable, is consistent with ZF.
17.
18.
19.
Joaquim Martín 《Journal of Mathematical Analysis and Applications》2008,344(1):99-123
We prove new extended forms of the Pólya-Szegö symmetrization principle in the fractional case. As a consequence we determine new results for rearrangement invariant hulls of generalized Besov spaces. 相似文献
20.
We prove new extended forms of the Pólya-Szegö symmetrization principle. As a consequence new sharp embedding theorems for generalized Sobolev and Besov spaces are proved. 相似文献