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1.
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
2.
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
3.
Ariyadasa Aluthge 《Integral Equations and Operator Theory》1996,24(4):497-501
A bounded linear operatorT is calledp-Hyponormal if (T
*T)p(TT
*)p, 0<p1. In Aluthge [1], we studied the properties of p-hyponormal operators using the operator
. In this work we consider a more general operator
, and generalize some properties of p-hyponormal operators obtained in [1]. 相似文献
4.
Eungil Ko 《Integral Equations and Operator Theory》2007,57(4):567-582
The backward Aluthge iterate (defined below) of a hyponormal operator was initiated in [11]. In this paper we characterize
the backward Aluthge iterate of a weighted shift. Also we show that the backward Aluthge iterate of a hyponormal operator
has an analogue of the single valued extension property for
. Finally, we show that backward Aluthge iterates of a hyponormal operator have scalar extensions. As a corollary, we get
that the backward Aluthge iterate of a hyponormal operator has a nontrivial invariant subspace if its spectrum has interior
in the plane. 相似文献
5.
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
6.
Spectral pictures of Aluthge transforms of operators 总被引:4,自引:0,他引:4
In this paper we continue our study, begun in [12], of the relationships between an arbitrary operatorT on Hilbert space and its Aluthge transform
. In particular, we show that in most cases the spectral picture ofT coincides with that of
, and we obtain some interesting connections betweenT and
as a consequence. 相似文献
7.
Eungil Ko 《Integral Equations and Operator Theory》2007,59(2):173-187
In this paper, we consider the special case of the question raised by Halmos (see below). In particular, we show that if Tk is p-hyponormal, then T is a subscalar operator of order 4k. As a corollary, we obtain that if Tk is p-hyponormal and σ(T) has nonempty interior in the plane, then T has a nontrivial invariant subspace. 相似文献
8.
Let n be a positive integer, an operator T belongs to class A(n) if , which is a generalization of class A and a subclass of n-paranormal operators, i.e., for unit vector x. It is showed that if T is a class A(n) or n-paranormal operator, then the spectral mapping theorem on Weyl spectrum of T holds. If T belongs to class A(n), then the nonzero points of its point spectrum and joint point spectrum are identical, the nonzero points of its approximate
point spectrum and joint approximate point spectrum are identical.
This work is supported by the Innovation Foundation of Beihang University (BUAA) for PhD Graduate, National Natural Science
Fund of China (10771011) and National Key Basic Research Project of China Grant No. 2005CB321902. 相似文献
9.
Vincent Cachia Hagen Neidhardt Valentin A. Zagrebnov 《Integral Equations and Operator Theory》2001,39(4):396-412
We study the operator-norm error bound estimate for the exponential Trotter product formula in the case of accretive perturbations. LetA be a semibounded from below self-adjoint operator in a separable Hilbert space. LetB be a closed maximal accretive operator such that, together withB
*, they are Kato-small with respect toA with relative bounds less than one. We show that in this case the operator-norm error bound estimate for the exponential Trotter product formula is the same as for the self-adjointB [12]:
We verify that the operator—(A+B) generates a holomorphic contraction semigroup. One gets similar results whenB is substituted byB
*.To the memory of Tosio Kato 相似文献
10.
Amitai Regev 《Israel Journal of Mathematics》1977,26(2):105-125
LetK = To(s3), {cn} its codimensions, {ln} its colengths and {Χn} its sequence of co-characters. For 9≦n, cn =2n - 1 or cn =n(n + l)/2- 1, 3≦ln ≦4 and χn =[n] + 2[n-1,1] + α[n-2,2] + β[22,1n?4] where α + β≦l. 相似文献
11.
For the unilateral shift operator U on the Hardy space H2(T), we describe conditions on operators T, acting on H2(T), that are necessary and sufficient for the pair (U, T) to be jointly hyponormal. One necessary condition is that T be a Toeplitz operator. Consequently, we study certain nonanalytic symbols that give rise to Toeplitz operators hyponormal with the shift, and thereby obtain examples of noncommuting, jointly hyponormal pairs.Supported in part by a research grant from NSERC 相似文献
12.
LetR andS be bounded linear operators on a Bananch space. We discuss the spectral and subdecomposable properties and properties concerning invariant subspaces common toRS andSR. We prove that, by these properties,p-hyponormal and log-hyponormal operators and their generalized Aluthge transformations are all subdecomposable operators;T andT(r, 1–r)(0<r<1) have same spectral structure and equal spectral parts ifT denotesp-hyponormal or dominant operator; for everyT L(H), 0<r<1,T has nontrivial (hyper-)invariant subspace ifT(r, 1–r) does.This research was supported by the National Natural Science Foundation of China. 相似文献
13.
Atsushi Uchiyama 《Integral Equations and Operator Theory》1999,34(1):91-106
For an operatorT satisfying thatT
*(T
*
T–TT
*)T0, we shall show that and, moreover, tr
itT isn-multicyclic.For an operatorT satisfying thatT
*
{(T
*
T)
p
–(TT
*)
p
}T0 for somep (0, 1], we shall show that
and, moreover,
ifT isn-multicyclic. 相似文献
14.
For a Riesz operator T on a reflexive Banach space X with nonzero eigenvalues
denote by E(λi; T) the eigen-projection corresponding to an eigenvalue λi. In this paper we will show that if the operator sequence
is uniformly bounded, then the Riesz operator T can be decomposed into the sum of two operators Tp and Tr: T = Tp + Tr, where Tp is the weak limit of Tn and Tr is quasi-nilpotent. The result is used to obtain an expansion of a Riesz semigroup T(t) for t ≥ τ. As an application, we consider the solution of transport equation on a bounded convex body. 相似文献
15.
In this paper, we reprove that: (i) the Aluthge transform of a complex symmetric operator
[(T)\tilde] = |T|\frac12 U|T|\frac12\tilde{T} = |T|^{\frac{1}{2}} U|T|^{\frac{1}{2}} is complex symmetric, (ii) if T is a complex symmetric operator, then ([(T)\tilde])*(\tilde{T})^{*} and [(T*)\tilde]\widetilde{T^{*}} are unitarily equivalent. And we also prove that: (iii) if T is a complex symmetric operator, then [((T*))\tilde]s,t\widetilde{(T^{*})}_{s,t} and ([(T)\tilde]t,s)*(\tilde{T}_{t,s})^{*} are unitarily equivalent for s, t > 0, (iv) if a complex symmetric operator T belongs to class wA(t, t), then T is normal. 相似文献
16.
Let T be a bounded linear
operator on a complex Hilbert space H.
T $/in$ B(H)
is called a log-hyponormal operator if T
is invertible and log (TT
*) log (T
*
T).
Since a function log : (0,) (-,) is operator
monotone, every invertible p-hyponormal operator T, i.e., (TT
*)
p
(T
*
T
p
is log-hyponormal for 0 < p 1. Putnams inequality for p-hyponormal operator
T is the following:$ \| (T^*T)^p-(TT^*)^p \|\leq\frac{p}{\pi}\int\int_{\sigma(T)}r^{2p-1}drd\theta $.In this paper, we prove that if T is log-hyponormal, then$ \| log(T^*T)-log(TT^*) \|\leq\frac{1}{\pi}\int\int_{\sigma(T)}r^{-1}drd\theta $. 相似文献
17.
Given an r×r complex matrix T, if T=U|T| is the polar decomposition of T, then, the Aluthge transform is defined byΔ(T)=|T|1/2U|T|1/2. Let Δn(T) denote the n-times iterated Aluthge transform of T, i.e., Δ0(T)=T and Δn(T)=Δ(Δn−1(T)), n∈N. We prove that the sequence {Δn(T)}n∈N converges for every r×r matrix T. This result was conjectured by Jung, Ko and Pearcy in 2003. We also analyze the regularity of the limit function. 相似文献
18.
Laurian Suciu 《Integral Equations and Operator Theory》2006,56(2):285-299
The current article pleads for the possibility to obtain an orthogonal decomposition of a Hilbert space
which is induced by a regular A-contraction defined in [9, 10], A being a positive operator on
. The decomposition generalizes the well-known decomposition related to a contraction T of
, which gives the ergodic character of T. This decomposition is being used to prove certain versions for regular A-contractions of the mean ergodic theorem, as well as a version of Patil’s theorem from [8]. Also, we characterize the solutions
of corresponding functional equations in the range of A1/2, by analogy with the result of Lin-Sine in [7]. 相似文献
19.
On log-hyponormal operators 总被引:9,自引:0,他引:9
Kôtarô Tanahashi 《Integral Equations and Operator Theory》1999,34(3):364-372
LetTB(H) be a bounded linear operator on a complex Hilbert spaceH.TB(H) is called a log-hyponormal operator itT is invertible and log (TT
*)log (T
*
T). Since log: (0, )(–,) is operator monotone, for 0<p1, every invertiblep-hyponormal operatorT, i.e., (TT
*)
p
(T
*
T)
p
, is log-hyponormal. LetT be a log-hyponormal operator with a polar decompositionT=U|T|. In this paper, we show that the Aluthge transform
is
. Moreover, ifmeas ((T))=0, thenT is normal. Also, we make a log-hyponormal operator which is notp-hyponormal for any 0<p.This research was supported by Grant-in-Aid Research No. 10640185 相似文献
20.
A bounded operatorT is called cellular-indecomposable ifL M {0} wheneverL andM are nonzero invariant subspaces forT. We prove that a cyclic subnormal operator is cellular-indecomposable if and only if it is quasi-similar to an analytic Toeplitz operator whose symbol is a weak-star generator ofH
. This completes our previous work [5], [6]. 相似文献