The Square Root Problem and Aluthge transforms of weighted shifts
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DOI: 10.1002/mana.201600302
Abstract: In this paper we consider the following question. When does there exist a square root of a probability measure supported on R+? This question is naturally related to subnormality of weighted shifts. The main result… read more here.
Keywords: probability; square root; aluthge; measure ... See more keywords
(A, m)-Isometric Unilateral Weighted Shifts in Semi-Hilbertian Spaces
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DOI: 10.1007/s40840-016-0307-5
Abstract: For a positive integer m, a bounded linear operator T on a Hilbert space $$\mathbb {H}$$H is called an (A, m)-isometry, if $$\Theta ^{(m)}_{A}(T) =\sum _{k=0}^{m}(-1)^{m-k}{m\atopwithdelims ()k}T^{*k}AT^{k}=0$$ΘA(m)(T)=∑k=0m(-1)m-kmkT∗kATk=0, where A is a positive (semi-definite) operator. In this… read more here.
Keywords: unilateral weighted; isometric unilateral; weighted shifts; shifts semi ... See more keywords
The Wold-Type Decomposition for m-Isometries
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DOI: 10.1007/s40840-021-01129-4
Abstract: The aim of this paper is to study the Wold-type decomposition in the class of m-isometries. One of our main results establishes an equivalent condition for an analytic m-isometry to admit the Wold-type decomposition for… read more here.
Keywords: decomposition isometries; wold type; weighted shifts; type decomposition ... See more keywords
Existence of non-subnormal completely semi-weakly hyponormal weighted shifts
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DOI: 10.2298/fil1706627l
Abstract: In this paper, we introduce a new notion of completely semi-weakly hyponormal operator which is a special case of polynomially hyponormal operator. For an one-step backward extension of the Bergman weighted shift, we show that… read more here.
Keywords: completely semi; semi weakly; hyponormal weighted; weakly hyponormal ... See more keywords