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1.
Stephan Ramon Garcia 《Integral Equations and Operator Theory》2008,60(3):357-367
If denotes the polar decomposition of a bounded linear operator T, then the Aluthge transform of T is defined to be the operator . In this note we study the relationship between the Aluthge transform and the class of complex symmetric operators (T iscomplex symmetric if there exists a conjugate-linear, isometric involution so that T = CT*C). In this note we prove that: (1) the Aluthge transform of a complex symmetric operator is complex symmetric, (2) if T is complex symmetric, then and are unitarily equivalent, (3) if T is complex symmetric, then if and only if T is normal, (4) if and only if T
2 = 0, and (5) every operator which satisfies T
2 = 0 is necessarily complex symmetric.
This work partially supported by National Science Foundation Grant DMS 0638789. 相似文献
2.
In this note we give an example of an ∞-hyponormal operator T whose Aluthge transform
is not (1+ɛ)-hyponormal for any ɛ > 0 and show that the sequence
of interated Aluthge transforms of T need not converge in the weak operator topology, which solve two problems in [6]. 相似文献
3.
We shall give some results on generalized aluthge transformation for p-hyponormal and log-hyponormal operators.We shall also discuss the best possibility of these results. 相似文献
4.
An operator \({T\in{\mathcal{L}}({\mathcal{H}})}\) is said to be complex symmetric if there exists a conjugation C on \({{\mathcal H}}\) such that \({T= CT^{\ast}C}\). In this paper, we study the spectral radius algebras for complex symmetric operators. In particular, we prove that if A is a complex symmetric operator, then the spectral radius algebra \({{\mathcal B}_{A}}\) associated with A has a nontrivial invariant subspace under some conditions. Finally, we give some relations between \({P_{\tilde{A}}}\) and \({P_{\widetilde{A^{\ast}}}}\) (defined below) when A is complex symmetric. 相似文献
5.
In this note we study the k-hyponormality and the subnormality of Aluthge transforms of weighted shifts. It is shown that Aluthge transforms of weighted
shifts need not preserve the k-hyponormality. Moreover, we show that if W
α
is a subnormal weighted shift with 2-atomic Berger measure then its Aluthge transform [(W)\tilde]a{\widetilde{W}_\alpha} is subnormal if and only if at least one of two atoms is zero. 相似文献
6.
A conjugation C is antilinear isometric involution on a complex Hilbert space , and is called complex symmetric if T* = CTC for some conjugation C. We use multiplicity theory to describe all conjugations commuting with a fixed positive operator. We expand upon a result
of Garcia and Putinar to provide a factorization of complex symmetric operators which is based on the polar decomposition.
This paper is based in part on the first author’s Master’s Project. 相似文献
7.
We pose three questions about the structure and application of complex symmetric operators. 相似文献
8.
证明了在复对称算子的前提下,对数-亚正规算子与正规算子是等价的,并且给出了复对称算子的一些等价性质;最后通过给出例子来说明我们的结论. 相似文献
9.
Approximate solutions to problems from quantum scattering theoryand the theory of gauge invariance are obtained. The methodused is a variational-iterative technique applied to operatorson a complex space, not necessarily with a discrete spectrum. 相似文献
10.
Analysis of Non-normal Operators via Aluthge Transformation 总被引:1,自引:0,他引:1
Let T be a bounded linear operator on a complex Hilbert space
. In this paper, we show that T has Bishops property () if and only if its Aluthge transformation
has property (). As applications, we can obtain the following results. Every w-hyponormal operator has property (). Quasi-similar w-hyponormal operators have equal spectra and equal essential spectra. Moreover, in the last section, we consider Chs problem that whether the semi-hyponormality of T implies the spectral mapping theorem Re(T) = (Re T) or not. 相似文献
11.
Let T be a bounded linear operator on an infinite dimensional complex Hilbert space. In this paper, we introduce the new class, denoted ${{\mathcal{QP}}}$ , of operators satisfying ${{\|T^{2}x\|^{2}\leq \|T^{3}x\|\|Tx\|}}$ for all ${{x \in \mathcal{H}}}$ . This class includes the classes of paranormal operators and quasi-class A operators. We prove basic structural properties of these operators. Using these results, we also prove that if E is the Riesz idempotent for a nonzero isolated point λ0 of the spectrum of ${{T \in \mathcal{QP}}}$ , then E is self-adjoint if and only if ${{N(T-\lambda_{0}) \subseteq N(T^{*}-\overline{\lambda}_{0})}}$ . 相似文献
12.
利用矩阵的Kronecker积给出了中心对称矩阵的若干特征,并讨论了由特征值和特征向量反构中心对称矩阵的问题. 相似文献
13.
Der Chen CHANG Jing Zhi TIE 《数学学报(英文版)》2005,21(4):803-818
In this note, we compute the fundamental solution for the Hermite operator with singularity at an arbitrary point y∈R^n. We also apply this result to obtain the fundamental solutions for the Grushin operator in R^2 and the sub-Laplacian in the Heisenberg group Hn. 相似文献
14.
In this note we show that if either T or T* is totally *-paranormal
then Weyls theorem holds for f(T) for every f
, and also a-Weyls theorem holds for f(T) if T is totally *-paranormal. We prove that if either
T or T* is *-paranormal then the spectral mapping theorem holds for the
Weyl spectrum and for the essential approximate point spectrum. 相似文献
15.
Björn G. Walther 《Journal of Fourier Analysis and Applications》2014,20(6):1328-1337
Let \({\mathcal {F}}f\) be an abolutely convergent Fourier transform on the real line. We extend the following result of K. Karlander to \({\mathbf {R}^{n}}\) for \(n \ge 1\) : Any closed reflexive subspace \(\{ {\mathcal {F}}f \}\) of the space of continuous functions vanishing at infinity is of finite dimension. 相似文献
16.
Let B(H) denote the algebra of operators on a complex separable
Hilbert space H, and let A $\in$ B(H) have the polar decomposition A = U|A|.
The Aluthge transform
is defined to be the operator
.
We say that A $\in$ B(H) is p-hyponormal,
.
Let
.
Given p-hyponormal
, such that AB is compact, this
note considers the relationship between
denotes an enumeration in decreasing order repeated according
to multiplicity of the eigenvalues of the
compact operator T (respectively,
singular values of the compact operator T).
It is proved that
is bounded above by
and below by
for all j = 1, 2, . . .
and that if also
is normal, then there exists a unitary
U1 such that
for all j = 1, 2, . . .. 相似文献
17.
The notion of a polar wavelet transform is introduced. The underlying non-unimodular Lie group, the associated square-integrable
representations and admissible wavelets are studied. The resolution of the identity formula for the polar wavelet transform
is then formulated and proved. Localization operators corresponding to the polar wavelet transforms are then defined. It is
proved that under suitable conditions on the symbols, the localization operators are, in descending order of complexity, paracommutators,
paraproducts and Fourier multipliers.
This research was supported by the Natural Sciences and Engineering Research Council of Canada. 相似文献
18.
19.
S. M. Patel 《Mathematische Nachrichten》1977,78(1):357-361
The aim of this note is to study the spectral properties of the LUECKE's class R of operators T such that ‖(T – zI)?1‖=1/d(z, W(T)) for all z?CLW(T), where CLW(T) is the closure of the numerical range W(T) of T and d(z, W(T)) is the distance from z to W(T). The main emphasis is on the investigation of those properties of operators of class R which are either similar to or distinct from those of operators satisfying the growth condition (G1). 相似文献
20.
A Note on Positivity of Elementary Operators 总被引:1,自引:0,他引:1
We show that operators on n x n matrices which are representablein the form (where ai andbi are n x n matrices) and are k-positive for must be completely positive. As a consequence, elementaryoperators on a C*-algebra with minimal length l which are k-positivefor must be completely positive. 1991 Mathematics Subject Classification 47B47, 46L05, 47B65. 相似文献