共查询到20条相似文献,搜索用时 15 毫秒
1.
Isao Saito 《Integral Equations and Operator Theory》1992,15(5):864-878
We improve the result of C. C. Huang about self-dual subnormal operators, and consider the converse of this result. 相似文献
2.
3.
Jan Stochel 《Integral Equations and Operator Theory》2002,43(2):189-214
Various theorems on lifting strong commutants of unbounded subnormal (as well as formally subnormal) operators are proved. It is shown that the strong symmetric commutant of a closed symmetric operatorS lifts to the strong commutant of some tight selfadjoint extension ofS. Strong symmetric commutants of orthogonal sums of subnormal operators are investigated. Examples of (unbounded) irreducible subnormals, pure subnormals with rich strong symmetric commutants and cyclic subnormals with highly nontrivial strong commutants are discussed.This work was supported by the KBN grant # 2P03A 041 10. 相似文献
4.
A bounded operator T is cellular-indecomposable if LnM{0} whenever L and M are any two nonzero invariant subspaces for T. We show that any such subnormal operator has a cyclic normal extension and is unitarily equivalent modulo the compact operators to an analytic Toeplitz operator whose symbol is a weak-star generator of H.Dedicated to the memory of James P. WilliamsThis work was supported in part by a grant from the National Science Foundation. 相似文献
5.
Daoxing Xia 《Integral Equations and Operator Theory》1993,17(3):417-439
Trace formulas are established for the product of commutators related to subnormal tuple of operators (S
1,...,S
n
) with minimal normal extension (N
1,...,N
n
) satisfying conditions that sp(S
j
)/sp(N
j
) is simply-connected with smooth boundary Jordan curve sp(N
i
) and [S
j
*
,S
j
]1/2 L
1,j=1, 2,...,n.Some complete unitary invariants related to the trace formulas are found.This work is supported in part by NSF Grant no. DMS-9101268. 相似文献
6.
This work continues that begun in [9]. Our investigation has led us to the following conjecture: 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 of H. In this paper some particular cases of the conjecture are verified.This work was supported in part by a grant from the National Science Foundation. 相似文献
7.
Daoxing Xia 《Integral Equations and Operator Theory》1996,24(1):106-125
In this paper, we study the model of a pure subnormal operator with finite rank self-commutator and of the relatedn-tuple of commuting linear bounded operators. We also give some applications of the model to the theory ofn-tuples of commuting operators with trace class self-commutators.This work is supported in part by a NSF grant no. DMS-9400766. 相似文献
8.
Daoxing Xia 《Integral Equations and Operator Theory》2000,37(4):487-504
In this paper, a functional model of rank one perturbation of the Heisenberg commutation relation is established. In some cases, it turns out to be unbounded subnormal. 相似文献
9.
Caixing Gu 《Journal of Functional Analysis》2004,215(1):178-205
Let X be a bounded linear operator on the Hardy space H2 of the unit disk. We show that if is of finite rank for every inner function θ, then X=T?+F for some Toeplitz operator T? and some finite rank operator F on H2. This solves a variant of an open question where the compactness replaces the finite rank conditions. 相似文献
10.
Nathan S. Feldman 《Integral Equations and Operator Theory》2000,37(4):402-422
We study pure subnormal operators whose self-commutators have zero as an eigenvalue. We show that various questions in this are closely related to questions involving approximation by functions satisfying
and to the study ofgeneralized quadrature domains.First some general results are given that apply to all subnormal operators within this class; then we consider characterizing the analytic Toeplitz operators, the Hardy operators and cyclic subnormal operators whose self-commutators have zero as an eigenvalue. 相似文献
11.
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
12.
Atsushi Uchiyama 《Integral Equations and Operator Theory》1999,33(2):221-230
For an-multicyclicp-hyponormal operatorT, we shall show that |T|2p
–|T
*|2p
belongs to the Schatten
and that tr
Area ((T)). 相似文献
13.
Angular cutting for log-hyponormal operators 总被引:1,自引:0,他引:1
We define an angular section for a log-hyponormal operator on a Hilbert space, cut by an arc on the unit circle, and establish various spectral properties for it, which correspond to the properties of an angular section for ap-hyponormal opertor.Dedicated to Professor Norio Shimakura on the occasion of his sixtieth birthdayThis research was supported by Grant-in-Aid Research 1 No. 12640187. 相似文献
14.
B. P. Duggal 《Integral Equations and Operator Theory》1996,26(3):338-345
IfA
i
i=1, 2 are quasi-similarp-hyponormal operators such thatUi is unitary in the polar decompositionA
i
=U
i
|A
i
|, then (A
1)=(A
2) and
c(A1) = e(A2). Also a Putnam-Fuglede type commutativity theorem holds for p-hyponomral operators. 相似文献
15.
James Zhijian Qiu 《Integral Equations and Operator Theory》1997,27(3):334-346
Let denote the set of analytic bounded point evaluations forR
q
(K, ). Assume that
. In this paper, we first show that if is a finitely connected domain and if the evaluation map fromR
q
(K, )L
() toH
() is surjective, then | is absolutely continuous with respect to harmonic measure for . This generalizes Olin and Yang's corresponding result for polynomials and the proof we present here is simpler. We also provide an example that shows this absolute continuity property fails in general when is an infinitely connected domain. In the second part, we then offer a solution to a problem of Conway and Elias. 相似文献
16.
17.
A continuation of the study of thew-hyponormal operators is presented. It is shown thatw-hyponormal operators are paranormal. Sufficient conditions which implyw-hyponormal operators are normal are given. The nonzero points of the approximate and joint approximate point spectra are shown to be identical forw-hyponormal operators. The square of an invertiblew-hyponormal operator is shown to bew-hyponormal. 相似文献
18.
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
19.
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
20.
We prove that every one dimensional extension of a separably acting normal operator has a cyclic commutant, and that every non-algebraic normal operator has a two-dimensional extension which fails to have a cyclic commutant. Contrasting this, we prove that ifT is an extension of a normal operator by an algebraic operator then the weakly closed algebraW(T) has a separating vector.Partially supported by NSF Grant DMS-9107137 相似文献