共查询到20条相似文献,搜索用时 15 毫秒
1.
Roman Drnovsek 《Proceedings of the American Mathematical Society》1997,125(4):1081-1087
The concept of quasispectral maximal subspaces for quasinilpotent (but not nilpotent) operators was introduced by M. Omladi\v{c} in 1984. As an application a class of quasinilpotent operators on -spaces, close to the Volterra kernel operator, was studied. In the present Banach function space setting we determine all quasispectral maximal subspaces of analogues of such operators and prove that these subspaces are all the invariant bands. An example is given showing that (in general) they are not all the closed, invariant ideals of the operator.
2.
Roman Drnovsek 《Proceedings of the American Mathematical Society》2007,135(12):3833-3836
Let be a positive operator on a complex Banach lattice. We prove that is greater than or equal to the identity operator if
3.
Isabelle Chalendar Jonathan R. Partington 《Proceedings of the American Mathematical Society》2006,134(5):1391-1396
Let be a separable Banach space and a sequence of closed subspaces of satisfying for all . We first prove the existence of a dense-range and injective compact operator such that each is a dense subset of , solving a problem of Yahaghi (2004). Our second main result concerns isomorphic and dense-range injective compact mappings between dense sets of linearly independent vectors, extending a result of Grivaux (2003).
4.
Let
be the quasinilpotent operator without an invariant subspace constructed by C. J. Read. We prove that the modulus of this operator has an invariant subspace (and even an eigenvector). This answers a question posed by Y. Abramovich, C. Aliprantis and O. Burkinshaw. 相似文献
5.
A. Fernández Valles 《Proceedings Mathematical Sciences》2006,116(3):317-323
In this article we obtain some positive results about the existence of a common nontrivial invariant subspace forN-tuples of not necessarily commuting operators on Banach spaces with a Schauder basis. The concept of joint quasinilpotence
plays a basic role. Our results complement recent work by Kosiek [6] and Ptak [8]. 相似文献
6.
7.
Evgeny AbakumovAlexander Borichev 《Journal of Functional Analysis》2002,188(1):1-26
We construct right shift invariant subspaces of index n, 1?n?∞, in ?p spaces, 2<p<∞, and in weighted ?p spaces. 相似文献
8.
Bands in lattices of operators 总被引:1,自引:0,他引:1
C. B. Huijsmans A. W. Wickstead 《Proceedings of the American Mathematical Society》1996,124(12):3835-3841
We consider the lattice of regular operators on a Dedekind complete Banach lattice. We show that in general the projection onto a band generated by a lattice homomorphism need not be continuous and that the principal bands need not be closed for the operator norm. In fact it is possible to find a convergent sequence of operators all the members of which are disjoint from the limit.
9.
研究了闭极大三角代数的对角不交理想中有限秩算子的性质,并利用这些性质讨论了几种特殊的对角不交理想 相似文献
10.
Ami Viselter 《Semigroup Forum》2009,79(2):355-368
A spectral integral representation is established for locally defined symmetric semigroups of operators, with indices which are not restricted to a neighborhood of zero. This extends the well-known results of Fröhlich (Adv. Appl. Math. 1:237–256, 1980) and Klein and Landau (J. Funct. Anal. 44:121–137, 1981). 相似文献
11.
Lutz Weis 《Proceedings of the American Mathematical Society》1998,126(11):3253-3256
We give a short proof showing that the growth bound of a positive semigroup on equals the spectral bound of its generator. It is based on a new boundedness theorem for positive convolution operators on . We also give a counterexample, showing that Gearhart's result does not extend from Hilbert spaces to -spaces.
12.
There is a subtle difference as far as the invariant subspace problem is concerned for operators acting on real Banach spaces
and operators acting on complex Banach spaces. For instance, the classical hyperinvariant subspace theorem of Lomonosov [Funktsional. Anal. nal. i Prilozhen 7(3)(1973), 55–56. (Russian)], while true for complex Banach spaces is false for real Banach spaces. When one starts with a
bounded operator on a real Banach space and then considers some “complexification technique” to extend the operator to a complex
Banach space, there seems to be no pattern that indicates any connection between the invariant subspaces of the “real” operator
and those of its “complexifications.” The purpose of this note is to examine two complexification methods of an operator T acting on a real Banach space and present some questions regarding the invariant subspaces of T and those of its complexifications
Mathematics Subject Classification 1991: 47A15, 47C05, 47L20, 46B99
Y.A. Abramovich: 1945–2003
The research of Aliprantis is supported by the NSF Grants EIA-0075506, SES-0128039 and DMI-0122214 and the DOD Grant ACI-0325846 相似文献
13.
The main results obtained are:– A Dedekind complete Banach lattice Y has a Fatou norm if and only if, for any Banach lattice X, the regular-norm unit ball Ur = {T Lr(X,Y): ||T||r 1} is closed in the strong operator topology on the space of all regular operators, Lr(X,Y).– A Dedekind complete Banach lattice Y has a norm which is both Fatou and Levi if and only if, for any Banach lattice X, the regular-norm unit ball Ur is closed in the strong operator topology on the space of all bounded operators, L(X,Y).– A Banach lattice Y has a Fatou–Levi norm if and only if for every L-space X the space L(X,Y) is a Banach lattice under the operator norm.– A Banach lattice Y is isometrically order isomorphic to C(S) with the supremum norm, for some Stonean space S, if and only if, for every Banach lattice X, L(X,Y) is a Banach lattice under the operator norm.Several examples demonstrating that the hypotheses may not be removed, as well as some applications of the results obtained to the spaces of operators are also given. For instance:– If X = Lp() and Y = Lq(), where 1 < p,q < , then Lr(X,Y) is a first category subset of L(X,Y). 相似文献
14.
We study conditions on an infinite dimensional separable Banach space X implying that X is the only non-trivial invariant subspace of X** under the action of the algebra
of biconjugates of bounded operators on
. Such a space is called simple. We characterize simple spaces among spaces which contain an isomorphic copy of c
0, and show in particular that any space which does not contain ℓ1 and has property (u) of Pelczynski is simple. 相似文献
15.
During the last few years the authors have studied extensively the invariant subspace problem of positive operators; see [6] for a survey of this investigation. In [4] the authors introduced the class of compact-friendly operators and proved for them a general theorem on the existence of invariant subspaces. It was then asked if every positive operator is compact-friendly. In this note, we present an example of a positive operator which is not compact-friendly but which, nevertheless, has a non-trivial closed invariant subspace.In the process of presenting this example, we also characterize the multiplication operators that commute with non-zero finite-rank operators. We show, among other things, that a multiplication operator M
commutes with a non-zero finite-rank operator if and only the multiplier function is constant on some non-empty open set. 相似文献
16.
Verónica Dimant 《Linear and Multilinear Algebra》2019,67(2):248-266
We analyse the interplay between maximal/minimal/adjoint ideals of multilinear operators (between sequence spaces) and their associated Köthe sequence spaces. We establish relationships with spaces of multipliers and apply these results to describe diagonal multilinear operators from Lorentz sequence spaces. We also define and study some properties of the ideal of (E, p)-summing multilinear mappings, a natural extension of the linear ideal of absolutely (E, p)-summing operators. 相似文献
17.
18.
In this paper we study an application of nonlinear B‐bounded semigroups introduced in a previous paper. The application is similar to the particle transport problem which led to B‐bounded linear semigroups. We deal with a nonlinear particle transport problem, which can be solved by using B‐bounded nonlinear semigroups. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
19.
Fernanda Botelho James Jamison 《Proceedings of the American Mathematical Society》2008,136(4):1397-1402
We characterize generalized bi-circular projections on a minimal norm ideal of operators in where is a separable infinite dimensional Hilbert space.
20.
In this paper, we introduce the notion of generalized spherical Aluthge transforms for commuting pairs of operators and study nontrivial joint invariant (resp. hyperinvariant) subspaces between the generalized spherical Aluthge transform and the original commuting pair. Next, we study the norm continuity through generalized Aluthge transform maps. We also study how the Taylor spectra and the Fredrolm index of commuting pairs of operators behave under the spherical Duggal transform. Finally, we introduce the notion of Campbell binormality for commuting pairs of operators and investigate some of its basic properties under spherical Aluthge and Duggal transforms. Moreover, we obtain new set inclusion diagrams among normal, quasinormal, centered, and Campbell binormal commuting pairs of operators. 相似文献