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1.
《Mathematische Nachrichten》2017,290(5-6):840-851
It is well‐known that for a general operator T on Hilbert space, if T is subnormal, then is subnormal for all natural numbers . It is also well‐known that if T is hyponormal, then T 2 need not be hyponormal. However, for a unilateral weighted shift , the hyponormality of (detected by the condition for all ) does imply the hyponormality of every power . Conversely, we easily see that for a weighted shift is not hyponormal, therefore not subnormal, but is subnormal for all . Hence, it is interesting to note when for some , the subnormality of implies the subnormality of T . In this article, we construct a non trivial large class of weighted shifts such that for some , the subnormality of guarantees the subnormality of . We also prove that there are weighted shifts with non‐constant tail such that hyponormality of a power or powers does not guarantee hyponormality of the original one. Our results have a partial connection to the following two long‐open problems in Operator Theory: (i) characterize the subnormal operators having a square root; (ii) classify all subnormal operators whose square roots are also subnormal. Our results partially depend on new formulas for the determinant of generalized Cauchy–Hankel matrices and on criteria for their positive semi‐definiteness. 相似文献
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D. V. Yakubovich 《Integral Equations and Operator Theory》1995,23(3):353-371
In [6] (after Clancey's work [2]), Martin and Putinar introduced their two-dimensional functional model of a hyponormal operator, which reduces it to the multiplication by the independent variable in a space of distributions. Here we define another model which does (almost) the same for the adjoint operator. We also explain a close relation between these two models and dual bundle shift models of linear operators introduced in [13]. As application, an estimate of the effectual rational multiplicity of hyponormal operators is given.The research described in this publication was made possible in part by Grant No. NW8000 from the International Science Foundation 相似文献
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B. Yousefi 《Archiv der Mathematik》2004,83(6):536-539
Let
be a Hilbert space of functions analytic on a plane domain such that for every in the functional of evaluation at is bounded. Assume further that
contains the constants and admits multiplication by the independent variable z, Mz, as a bounded operator. We give sufficient conditions for Mz to be reflexive.Received: 17 February 2004 相似文献
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《Mathematische Nachrichten》2017,290(11-12):1612-1629
We show that a weighted shift on a directed tree is related to a multiplier algebra of coefficients of analytic functions. We use this relation to study spectral properties of the operator in question. 相似文献
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Victor Olevskii 《Integral Equations and Operator Theory》1996,25(4):496-500
We construct a continuous functionf on the circle such thatf is a Fourier multiplier inl
p
, 1<p<, but (x, y)=f(x–y) is not a Schur multiplier inS
p
,p2. 相似文献
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We investigate the spectral theory of the following general nonautonomous evolution equation
9.
Raúl E. Curto Sang Hoon Lee Woo Young Lee 《Integral Equations and Operator Theory》2002,44(2):138-148
In this article we provide an example of a Toeplitz operator which is 2-hyponormal but not subnormal, and we consider 2-hyponormal Toeplitz operators with finite rank self-commutators.Supported by NSF research grant DMS-9800931.Supported by KOSEF research project No. R01-2000-00003. 相似文献
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The Sz.-Nagy-FoiaŞ functional model for completely non-unitary contractions is extended to completely non-coisometric sequences
of bounded operatorsT = (T1,...,T
d) (d finite or infinite) on a Hilbert space, with bounded characteristic functions. For this class of sequences, it is shown
that the characteristic function θT is a complete unitary invariant.
We obtain, as the main result, necessary and sufficient conditions for a bounded multi-analytic operator on Fock spaces to
coincide with the characteristic function associated with a completely non-coisometric sequence of bounded operators on a
Hilbert space.
Research supported in part by a COBASE grant from the National Research Council.
The first author was partially supported by a grant from Ministerul Educaţiei Şi Cercetarii.
The second author was partially supported by a National Science Foundation grant. 相似文献
12.
《Quaestiones Mathematicae》2013,36(1):69-82
Abstract In this paper, the boundedness and compactness of the generalized composition operators and the products of Volterra type operators a nd composition operators between QK spaces are investigated. We also give a necessary condition for multiplication operators between QK spaces to be bounded or compact. 相似文献
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In the context of Köthe spaces we study the bases related with the backward unilateral weighted shift operator, the so-called generalized derivation operator, extending known results for spaces of analytic functions. These bases are a subclass of Sheffer sequences called generalized Appell sequences and they are closely connected with the isomorphisms invariant by the weighted shift. We use methods of the non classical umbral calculi to give conditions for a generalized Appell sequence to be a basis. 相似文献
15.
This paper is devoted to the question to obtain (algebraic and topologic) equivalence (after extension) relations between convolution type operators on unions of intervals and convolution type operators on the half-line. These operators are supposed to act between Bessel potential spaces,H
s,p
, which are the appropriate spaces in several applications. The present approach is based upon special properties of convenient projectors, decompositions and extension operators and the construction of certain homeomorphisms between the kernels of the projectors. The main advantage of the method is that it provides explicit operator matrix identities between the mentioned operators where the relations are constructed only by bounded invertible operators. So they are stronger than the (algebraic) Kuijper-Spitkovsky relation and the Bastos-dos Santos-Duduchava relation with respect to the transfer of properties on the prize that the relations depend on the orders of the spaces and hold only for non-critical orders:S – 1/p . For instance, (generalized) inverses of the operators are explicitly represented in terms of operator matrix factorization. Some applications are presented.This research was supported by Junta Nacional de Investigação Científica e Tecnológica (Portugal) and the Bundesminister für Forschung und Technologie (Germany) within the projectSingular Operators-new features and applications, and by a PRAXIS XXI project under the titleFactorization of Operators and Applications to Mathematical Physics. 相似文献
16.
Julio C. Ramos Fernández 《Quaestiones Mathematicae》2016,39(4):497-509
The objective of this paper is to use known properties of the associated weight to give new estimations of the norm and essential norm of the weighted com- position operators acting between weighted Banach spaces of analytic functions, in terms of composition with certain special functions in these spaces. As a consequence of our results, we obtain genuine extensions of a large number of recent results, and in particular, we extend classical results due to Montes-Rodríguez and Contreras and Hernández-Díaz. 相似文献
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Omar Hirzallah 《Linear algebra and its applications》2007,424(1):71-82
We prove several singular value inequalities and norm inequalities involving sums and direct sums of Hilbert space operators. It is shown, among other inequalities, that if X and Y are compact operators, then the singular values of are dominated by those of X ⊕ Y. Applications of these inequalities are also given. 相似文献