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1.
In the study of the gaps between subnormality and hyponormality both quadratic hyponormality and the related property positive
quadratic hyponormality have been considered, especially for weighted shift operators. In particular, these have been studied
for shifts with the first two weights equal and with Bergman tail or recursively generated tail. In this article, we characterize
the allowed first two equal weights for quadratic hyponormality with Bergman tail, and the allowed first two equal weights
for positive quadratic hyponormality with recursively generated tail.
相似文献
2.
Jaewoong Kim 《Linear and Multilinear Algebra》2017,65(6):1260-1275
In this paper, we study several properties for mono-weakly hyponormal 2-variable weighted shifts. First, we consider propagation phenomena for mono-weakly hyponormal (resp. mono-polynomially hyponormal) 2-variable weighted shifts. Next, we contemplate the mono-weak hyponormality under the Schur product. Finally, we study whether the mono-weak hyponormality is invariant under powers. 相似文献
3.
Jasang Yoon 《Journal of Mathematical Analysis and Applications》2007,333(2):626-641
In this paper we study the hyponormality and subnormality of 2-variable weighted shifts using the Schur product techniques in matrices. As applications, we generalize the result in [R. Curto, J. Yoon, Jointly hyponormal pairs of subnormal operators need not be jointly subnormal, Trans. Amer. Math. Soc. 358 (2006) 5135-5159, Theorem 5.2] and give a non-trivial, large class satisfying the Curto-Muhly-Xia conjecture [R. Curto, P. Muhly, J. Xia, Hyponormal pairs of commuting operators, Oper. Theory Adv. Appl. 35 (1988) 1-22] for 2-variable weighted shifts. Further, we give a complete characterization of hyponormality and subnormality in the class of flat, contractive, 2-variable weighted shifts T≡(T1,T2) with the condition that the norm of the 0th horizontal 1-variable weighted shift of T is a given constant. 相似文献
4.
George R. Exner Il Bong Jung Mi Ryeong Lee Sun Hyun Park 《Integral Equations and Operator Theory》2014,79(1):49-66
Given the weight sequence for a subnormal recursively generated weighted shift on Hilbert space, one approach to the study of classes of operators weaker than subnormal has been to form a backward extension of the shift by prefixing weights to the sequence. We characterize positive quadratic hyponormality and revisit quadratic hyponormality of certain such backward extensions of arbitrary length, generalizing earlier results, and also show that a function apparently introduced as a matter of convenience for quadratic hyponormality actually captures considerable information about positive quadratic hyponormality. 相似文献
5.
Takahiko Nakazi 《Proceedings of the American Mathematical Society》2008,136(7):2425-2428
The problem of hyponormality for Toeplitz operators with (trigo- nometric) polynomial symbols is studied. We give a necessary and sufficient condition using the zeros of the analytic polynomial induced by the Fourier coefficients of the symbol.
6.
We study a class of weighted shifts W
α defined by a recursively generated sequence α ≡ α0, … , α
m−2, (α
m−1, α
m
, α
m+1)∧ and characterize the difference between quadratic hyponormality and positive quadratic hyponormality. We show that a shift
in this class is positively quadratically hyponormal if and only if it is quadratically hyponormal and satisfies a finite
number of conditions. Using this characterization, we give a new proof of [12, Theorem 4.6], that is, for m = 2, W
α is quadratically hyponormal if and only if it is positively quadratically hyponormal. Also, we give some new conditions for
quadratic hyponormality of recursively generated weighted shift W
α (m ≥ 2). Finally, we give an example to show that for m ≥ 3, a quadratically hyponormal recursively generated weighted shift W
α need not be positively quadratically hyponormal. 相似文献
7.
Raú l Curto Sang Soo Park 《Proceedings of the American Mathematical Society》2003,131(9):2761-2769
We characterize -hyponormality and quadratic hyponormality of powers of weighted shifts using Schur product techniques.
8.
9.
§ 1.Introduction In [1 ] ,twooperatorclassesofD nearsubnormaloperatorsandnearsubnormaloperatorswereintroduced .TheelementarypropertiesofsuchoperatorswereobtainedbyuseoftheM Pgeneralizedinverse.Moreover,anewnecessaryandsufficientconditionforanoperatortobesubn… 相似文献
10.
We describe the Aluthge transform of an unbounded weighted composition operator acting in an L2-space. We show that its closure is also a weighted composition operator with the same symbol and a modified weight function. We investigate its dense definiteness. We characterize p-hyponormality of unbounded weighted composition operators and provide results on how it is affected by the Aluthge transformation. We show that the only fixed points of the Aluthge transformation on weighted composition operators are quasinormal ones. 相似文献
11.
Raú l E. Curto Jasang Yoon 《Transactions of the American Mathematical Society》2006,358(11):5139-5159
We construct three different families of commuting pairs of subnormal operators, jointly hyponormal but not admitting commuting normal extensions. Each such family can be used to answer in the negative a 1988 conjecture of R. Curto, P. Muhly and J. Xia. We also obtain a sufficient condition under which joint hyponormality does imply joint subnormality.
12.
Mustapha Raïssouli 《Linear and Multilinear Algebra》2019,67(2):213-220
Let T and S be two self-adjoint positive invertible operators of a complex Hilbert space H. In this paper, we investigate some inequalities involving the quadratic forms of the weighted arithmetic and harmonic means of T and S. Application for operator entropies is also discussed. 相似文献
13.
JueXian Li 《中国科学 数学(英文版)》2012,55(7):1441-1448
By using simultaneous triangularization technique, similarity for operator weighted shifts with finite multiplicity is characterized in terms of K0-group of commutant algebra. The result supports the conjecture posed by Cao et al. in 1999. Moreover, we discuss the relations between similarity and quasi-similarity for operator weighted shifts. 相似文献
14.
《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
15.
The problem whether Aluthge iteration of bounded operators on a Hilbert space H is convergent was introduced in [I. Jung, E. Ko, C. Pearcy, Aluthge transforms of operators, Integral Equations Operator Theory 37 (2000) 437-448]. And the problem whether the hyponormal operators on H with dimH=∞ has a convergent Aluthge iteration under the strong operator topology remains an open problem [I. Jung, E. Ko, C. Pearcy, The iterated Aluthge transform of an operator, Integral Equations Operator Theory 45 (2003) 375-387]. In this note we consider symbols with a fractional monotone property which generalizes hyponormality and 2-expansivity on weighted translation semigroups, and prove that if {St} is a weighted translation semigroup whose symbol has the fractional monotone property, then its Aluthge iteration converges to a quasinormal operator under the strong operator topology. 相似文献
16.
讨论单位圆盘中Dirichlet空间上Toeplitz算子的性质,给出了Dirichiet空间上以一类连续函数为符号的Toeplitz算子满足亚正规性的充分必要条件. 相似文献
17.
18.
William E. Hornor James E. Jamison 《Proceedings of the American Mathematical Society》1996,124(10):3123-3130
In this paper we investigate criterion for the hyponormality, cohyponormality, and normality of weighted composition operators acting on Hilbert spaces of vector-valued functions.
19.
In this paper we deal with the hyponormality of Toeplitz operators with matrix‐valued symbols. The aim of this paper is to provide a tractable criterion for the hyponormality of bounded‐type Toeplitz operators (i.e., the symbol is a matrix‐valued function such that Φ and are of bounded type). In particular, we get a much simpler criterion for the hyponormality of when the co‐analytic part of the symbol Φ is a left divisor of the analytic part. 相似文献
20.
Kit C. Chan 《Journal of Mathematical Analysis and Applications》2008,337(1):646-658
We examine common supercyclic vectors for a path of operators. In particular, we show that the path consisting of convex combinations of two arbitrary unilateral weighted backward shifts has a dense Gδ set of common supercyclic vectors. Moreover, we show there exists a path with a dense Gδ set of common supercyclic vectors between a unilateral weighted backward shift which satisfies the Supercyclicity Criterion, and an operator which does not. Lastly, we provide an example of a path of unilateral weighted backward shifts that fails to have a common supercyclic vector. 相似文献