Perturbations of weighted shifts
نویسندگان
چکیده
منابع مشابه
k-HYPONORMALITY OF FINITE RANK PERTURBATIONS OF UNILATERAL WEIGHTED SHIFTS
Abstract. In this paper we explore finite rank perturbations of unilateral weighted shifts Wα. First, we prove that the subnormality of Wα is never stable under nonzero finite rank pertrubations unless the perturbation occurs at the zeroth weight. Second, we establish that 2-hyponormality implies positive quadratic hyponormality, in the sense that the Maclaurin coefficients ofDn(s) := detPn [(W...
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In this paper, we study perturbations of multidimensional shifts of finite type. Specifically, for any Z shift of finite type X with d > 1 and any finite pattern w in the language of X, we denote by Xw the set of elements of X not containing w. For strongly irreducible X and patterns w with shape a d-dimensional cube, we obtain upper and lower bounds on h(X) − h(Xw) dependent on the size of w. ...
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(1) ‖p(T )‖ ≤M sup{|p(ζ)| : |ζ| = 1} ∀ polynomial p, and to be power bounded (notation T ∈ (PW)) if (1) holds for every polynomial of the special form p(ζ) = ζ where n is a positive integer. If T ∈ (PB) [resp., T ∈ (PW)], then there is a smallest number M which satisfies (1) [resp., (1) restricted]. This number will be called the polynomial bound of T [resp., the power bound of T ] and denoted ...
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An example is given of a unilateral weighted shift on complex Hubert space which is strictly cyclic but not strongly strictly cyclic. Similar examples of weighted shifts on the sequence spaces lp, for 1 < p < oo, are indicated.
متن کاملSubnormality of Bergman-like Weighted Shifts
For a, b, c, d ≥ 0 with ad − bc > 0, we consider the unilateral weighted shift S(a, b, c, d) with weights αn := √ an+b cn+d (n ≥ 0). Using Schur product techniques, we prove that S(a, b, c, d) is always subnormal; more generally, we establish that for every p ≥ 1, all p-subshifts of S(a, b, c, d) are subnormal. As a consequence, we show that all Bergman-like weighted shifts are subnormal.
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1974
ISSN: 0022-247X
DOI: 10.1016/0022-247x(74)90158-9