共查询到20条相似文献,搜索用时 15 毫秒
1.
Xiaoli Zhang 《Journal of Mathematical Analysis and Applications》2008,346(1):251-254
Let H be a complex Hilbert space and let B(H) denote the algebra of all bounded linear operators on H. For A,B∈B(H), the Jordan elementary operator UA,B is defined by UA,B(X)=AXB+BXA, ∀X∈B(H). In this short note, we discuss the norm of UA,B. We show that if dimH=2 and ‖UA,B‖=‖A‖‖B‖, then either AB∗ or B∗A is 0. We give some examples of Jordan elementary operators UA,B such that ‖UA,B‖=‖A‖‖B‖ but AB∗≠0 and B∗A≠0, which answer negatively a question posed by M. Boumazgour in [M. Boumazgour, Norm inequalities for sums of two basic elementary operators, J. Math. Anal. Appl. 342 (2008) 386-393]. 相似文献
2.
M. Barraa 《Proceedings of the American Mathematical Society》2005,133(6):1723-1726
Let and denote two -tuples of operators with and Let denote the elementary operators defined on the Hilbert-Schmidt class by We show that
Here is the essential numerical range, is the joint numerical range and is the joint essential numerical range.
Here is the essential numerical range, is the joint numerical range and is the joint essential numerical range.
3.
Hong-Ke Du Yue-Qing Wang Gui-Bao Gao 《Proceedings of the American Mathematical Society》2008,136(4):1337-1348
Let and , , be bounded linear operators acting on a separable Hilbert space . In this note, we prove that Moreover, we prove that there exists an operator with such that if and only if there exists a unitary such that
4.
P. Galindo T. W. Gamelin M. Lindströ m 《Transactions of the American Mathematical Society》2007,359(5):2109-2121
Let be a uniform algebra, and let be a self-map of the spectrum of that induces a composition operator on . The object of this paper is to relate the notion of ``hyperbolic boundedness' introduced by the authors in 2004 to the essential spectrum of . It is shown that the essential spectral radius of is strictly less than if and only if the image of under some iterate of is hyperbolically bounded. The set of composition operators is partitioned into ``hyperbolic vicinities" that are clopen with respect to the essential operator norm. This partition is related to the analogous partition with respect to the uniform operator norm.
5.
《Mathematische Nachrichten》2017,290(11-12):1678-1688
We investigate sufficient and necessary conditions for the space of bounded linear operators between two Banach spaces to be rough or average rough. Our main result is that is δ‐average rough whenever is δ‐average rough and Y is alternatively octahedral. This allows us to give a unified improvement of two theorems by Becerra Guerrero, López‐Pérez, and Rueda Zoca [J. Math. Anal. Appl. 427 (2015)]. 相似文献
6.
Pekka J. Nieminen 《Journal of Mathematical Analysis and Applications》2011,382(2):565-576
We derive exact formulas for the essential and weak essential norms of weighted analytic composition operators acting on certain function spaces in the unit disc, extending and improving earlier results due to Sarason and to Kriete and Moorhouse. Differences of composition operators are also considered. The formulas involve the Aleksandrov measures associated to the symbol of the operator. The results are based on a variant of a general method due to Weis of constructing best compact and weakly compact approximants for linear operators on L1 spaces. 相似文献
7.
T. Ando 《Linear algebra and its applications》2006,417(1):3-7
We determine the maximum in the class of unitarily invariant norms ∥·∥ such that w(A) ? ∥A∥ for all n-square matrices A. Here w(A) denotes the numerical radius of A. 相似文献
8.
It is shown that if is a compact operator on a Hilbert space with its numerical range contained in the closed unit disc and with intersecting the unit circle at infinitely many points, then is equal to . This is an infinite-dimensional analogue of a result of Anderson for finite matrices.
9.
Ying-Fen Lin 《Journal of Mathematical Analysis and Applications》2011,382(1):469-473
In this paper, we characterize surjective completely bounded disjointness preserving linear operators on Fourier algebras of locally compact amenable groups. We show that such operators are given by weighted homomorphisms induced by piecewise affine proper maps. 相似文献
10.
Stevo Stevi? 《Applied mathematics and computation》2010,216(1):187-10194
Let D be a bounded symmetric domain, H(D) the class of all holomorphic functions on D and u∈H(D). Operator norm of the multiplication operator on the weighted Bergman space , as well as of weighted composition operator from to a weighted-type space are calculated. 相似文献
11.
In this note we establish the best possible constant for the general lower estimate for the Jacobson - McCrimmon operator on the algebra of symmetric operators acting on a Hilbert space.
12.
The study of harmonic functions on a locally compact group G has recently been transferred to a “non-commutative” setting in two different directions: Chu and Lau replaced the algebra
L
∞(G) by the group von Neumann algebra VN(G) and the convolution action of a probability measure μ on L
∞(G) by the canonical action of a positive definite function σ on VN(G); on the other hand, Jaworski and the first author replaced L
∞(G) by to which the convolution action by μ can be extended in a natural way. We establish a link between both approaches. The action
of σ on VN(G) can be extended to . We study the corresponding space of “σ-harmonic operators”, i.e., fixed points in under the action of σ. We show, under mild conditions on either σ or G, that is in fact a von Neumann subalgebra of . Our investigation of relies, in particular, on a notion of support for an arbitrary operator in that extends Eymard’s definition for elements of VN(G). Finally, we present an approach to via ideals in , where denotes the trace class operators on L
2(G), but equipped with a product different from composition, as it was pioneered for harmonic functions by Willis.
M. Neufang was supported by NSERC and the Mathematisches Forschungsinstitut Oberwolfach.
V. Runde was supported by NSERC and the Mathematisches Forschungsinstitut Oberwolfach. 相似文献
13.
14.
Mohamed Barraa Mohamed Boumazgour 《Journal of Mathematical Analysis and Applications》2003,286(1):359-362
Let be the algebra of bounded linear operators on a Hilbert space H. For , define the elementary operator MA,B by MA,B(X)=AXB (). We give necessary and sufficient conditions for any pair of operators A and B to satisfy the equation ‖I+MA,B‖=1+‖A‖‖B‖, where I is the identity operator on H. 相似文献
15.
María J. Martín 《Journal of Mathematical Analysis and Applications》2005,304(1):22-32
We obtain new upper bounds on the norms of univalently induced composition operators acting on the Dirichlet space and compute explicitly the norms for univalent symbols whose range is the disk minus a set of measure zero. As an application, we show that the spectral radius of every univalently induced composition operator on the Dirichlet space is equal to one. 相似文献
16.
Bruce A. Barnes 《Proceedings of the American Mathematical Society》2007,135(6):1735-1740
Let be a bounded linear operator on a Banach space and let be a subspace of which is a Banach space and invariant. Denote by the restriction of to This paper explores the questions:
If the range of is closed, under what conditions is the range of closed?
If the range of is closed, under what conditions is the range of closed?
17.
In this paper, we express the essential norms of composition operators between weighted Bergman spaces of the unit disc in terms of the generalized Nevanlinna counting function. 相似文献
18.
19.
Ihab Al Alam 《Journal of Mathematical Analysis and Applications》2009,358(2):273-280
In this paper, we discuss the problem of compactness for weighted composition operators, defined on a Müntz space . We compute the essential norm of such operators on the Müntz spaces. As a corollary, we obtain the exact values of essential norms of composition and multiplication operators. 相似文献
20.
Bai Zhongzhi 《数学研究与评论》1998,(4)
1.IntroductionForapositivenumber1p∞andacomplexmatrixA=(aij)∈Cn×n,wedenoteby|A|p=ni,j=1|aij|p1pthelpnormofthematrixA,andbyA... 相似文献