共查询到20条相似文献,搜索用时 437 毫秒
1.
关于Banach空间算子的本性谱 总被引:1,自引:0,他引:1
这篇注记把文献[1]中关于希尔伯特空间算子本性谱特征刻划的某些结果推广到一般巴拿赫空间上去。其中之一是说明,零属于算子 T 的左本性谱的充分必要条件是存在一个紧算子 K,使得 T+K 的零空间无限维,或 R(T)不可补。 相似文献
2.
本文研究某些加权复合算子之非平凡不变子空间的存在性.特别地,证明了每个亚正规加权复合算子均有非平凡的不变子空间并且提出了一个新概念,称其为本性可逆变换.对于概率空间上本性可逆变换所确定的加权复合算子,给出其非平凡不变子空间存在性的一个等价刻画. 相似文献
3.
李觉先 《数学年刊A辑(中文版)》2003,(5)
本文研究某些加权复合算子之非平凡不变子空间的存在性。特别地,证明了每个亚正规加权复合算子均有非平凡的不变子空间并且提出了一个新概念,称其为本性可逆变换。对于概率空间上本性可逆变换所确定的加权复合算子,给出其非平凡不变子空间存在性的一个等价刻画。 相似文献
4.
讨论算子代数B(l∞)中各算子理想之间的关系,说明严格奇异算子理想S(l∞)与弱紧算子理想、也与非本性算子理想重合,成为B(L∞)中最大的、非平凡的闭算子理想;它们不与紧算子理想重合。 相似文献
5.
加权Herz空间上交换子的有界性 总被引:1,自引:0,他引:1
旨在建立一大类由BMO函数和线性算子所生成交换了在另权Herz空间上的有界性,这些线性算子包括Calderon-Zygmund奇异积分算子,带有粗糙核的R.Fefferman型奇积分算子和带有粗糙核的Ricci-Stein-振荡奇异积分算子。 相似文献
6.
一类次线性算子在广义Morrey空间上的加权有界性 总被引:1,自引:0,他引:1
本证明了如果次线性算子T在Orlicz空间上有介,则也有Morrey空间上有界,该算子包括极大算子和奇异积分算子等重要算子。 相似文献
7.
关于G-M成果研究的若干新动态Ⅱ--与G-M型空间相关的算子 总被引:2,自引:0,他引:2
结合自己的工作,对Gowers-Maurey系列成果获Fields奖以来的研究的新动态作一综述,该是下篇,主要讨论与G-M型空间相关的算子,包括可通过G-M型空间分解的算子,G-M型空间上的算子理想与算子构成,G-M型空间上的算子谱理论等。 相似文献
8.
利用导出映照的拉回测度和上极限,给出了单位球上Hardy空间上的复合算子的本性模的表示. 相似文献
9.
本文研究单位圆盘上Dirichlet型空间非紧Toeplitz算子的本性范数, 它事实上等于到紧Toeplitz算子集的距离. 并且这个距离可由无限多个紧Toeplitz算子来刻画, 这个结果与加权Bergman空间情形的类似. 相似文献
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11.
Julio Flores 《Journal of Mathematical Analysis and Applications》2009,354(2):657-663
The notion of disjointly homogeneous Banach lattice is introduced. In these spaces every two disjoint sequences share equivalent subsequences. It is proved that on this class of Banach lattices the product of a regular AM-compact and a regular disjointly strictly singular operators is always a compact operator. 相似文献
12.
Julio Flores 《Journal of Mathematical Analysis and Applications》2008,343(2):743-751
It is shown that every positive strictly singular operator T on a Banach lattice satisfying certain conditions is AM-compact and has invariant subspaces. Moreover, every positive operator commuting with T has an invariant subspace. It is also proved that on such spaces the product of a disjointly strictly singular and a regular AM-compact operator is strictly singular. Finally, we prove that on these spaces the known invariant subspace results for compact-friendly operators can be extended to strictly singular-friendly operators. 相似文献
13.
Julio Flores Francisco L. Hernández Evgueni M. Semenov Pedro Tradacete 《Israel Journal of Mathematics》2012,188(1):323-352
Compactness of the iterates of strictly singular operators on Banach lattices is analyzed. We provide suitable conditions
on the behavior of disjoint sequences in a Banach lattice, for strictly singular operators to be Dunford-Pettis, compact or
have compact square. Special emphasis is given to the class of rearrangement invariant function spaces (in particular, Orlicz
and Lorentz spaces). Moreover, examples of rearrangement invariant function spaces of fixed arbitrary indices with strictly
singular non power-compact operators are also presented. 相似文献
14.
Teresa Álvarez 《数学学报(英文版)》2010,26(8):1545-1554
Multivalued semi-Fredholm type linear operators with complemented ranges and null spaces are introduced. Conditions are obtained under which the classes given are stable under compact, strictly singular and strictly cosingular additive perturbations. 相似文献
15.
Eugeniu Spinu 《Journal of Mathematical Analysis and Applications》2011,383(2):259-264
We consider the following three closed algebraic ideals of operators on a Banach lattice: compact, strictly singular, and inessential operators. Suppose that 0?A?B and B is compact or strictly singular. We show that, under certain assumptions, A (or some power of A) is inessential. 相似文献
16.
Manuel González 《Journal of Mathematical Analysis and Applications》2005,305(1):53-62
We study the Fredholm theory for pairs of closed subspaces of a Banach space developed by Kato. We define the strictly singular and the strictly cosingular pairs of subspaces, and we show that some of the results of operator theory can be extended to this context. However, there are some notable differences. On the one hand, the perturbation classes problem has a positive answer in this context: the upper and lower semi-Fredholm pairs are stable under strictly singular and strictly cosingular perturbations, respectively, and this stability characterizes the strictly singular and the strictly cosingular pairs. Note that it has been proved recently that the perturbation classes problem for continuous semi-Fredholm operators has a negative answer. On the other hand, unlike in the case of operators, the Fredholm pairs are not stable under perturbation by strictly singular or strictly cosingular pairs. We also show the stability under composition of the compact, the strictly singular and the strictly cosingular pairs of subspaces. 相似文献
17.
We introduce a class of nonlinear continuous mappings in Banach spaces which allow us to characterize the Banach spaces without noncompact flat parts in their spheres as those that have the fixed point property for this type of mapping. Later on, we give an application to the existence of zeroes for certain kinds of accretive operators. 相似文献
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19.
《Indagationes Mathematicae》2017,28(6):1175-1182
In this work we introduce the disjointly improjective operators between Banach lattices. We investigate this class of operators. Also, we extend the Flores–Hernández’s theorem on the domination problem by disjoint strictly singular operator. 相似文献
20.
S. ter Horst M. Messerschmidt A.C.M. Ran M. Roelands M. Wortel 《Indagationes Mathematicae》2018,29(5):1350-1361
In recent years the coincidence of the operator relations equivalence after extension (EAE) and Schur coupling (SC) was settled for the Hilbert space case. For Banach space operators, it is known that SC implies EAE, but the converse implication is only known for special classes of operators, such as Fredholm operators with index zero and operators that can in norm be approximated by invertible operators. In this paper we prove that the implication EAE SC also holds for inessential Banach space operators. The inessential operators were introduced as a generalization of the compact operators, and include, besides the compact operators, also the strictly singular and strictly co-singular operators; in fact they form the largest ideal such that the invertible elements in the associated quotient algebra coincide with (the equivalence classes of) the Fredholm operators. 相似文献