1,121 research outputs found
Almost invariant half-spaces for operators on Hilbert space. II: operator matrices
This paper is a sequel to [6]. In that paper we transferred the discussions
in [1] and [13] concerning almost invariant half-spaces for operators on
complex Banach spaces to the context of operators on Hilbert space, and we gave
easier proofs of the main results in [1] and [13]. In the present paper we
discuss consequences of the above-mentioned results for the matricial structure
of operators on Hilbert space
Unbounded quasinormal operators revisited
Various characterizations of unbounded closed densely defined operators
commuting with the spectral measures of their moduli are established.In
particular, Kaufman's definition of an unbounded quasinormal operator is shown
to coincide with that given by the third-named author and Szafraniec. Examples
demonstrating the sharpness of results are constructed.Comment: 13 page
Unbounded subnormal weighted shifts on directed trees
A new method of verifying the subnormality of unbounded Hilbert space
operators based on an approximation technique is proposed. Diverse sufficient
conditions for subnormality of unbounded weighted shifts on directed trees are
established. An approach to this issue via consistent systems of probability
measures is invented. The role played by determinate Stieltjes moment sequences
is elucidated. Lambert's characterization of subnormality of bounded operators
is shown to be valid for unbounded weighted shifts on directed trees that have
sufficiently many quasi-analytic vectors, which is a new phenomenon in this
area. The cases of classical weighted shifts and weighted shifts on leafless
directed trees with one branching vertex are studied.Comment: 32 pages, one figur
On the structure of conditionally positive definite algebraic operators
Recently, the authors have introduced and intensively studied a class of bounded
Hilbert space operators called conditionally positive definite. Its origins go back to
the harmonic analysis on ∗-semigroups, namely to the concept of conditional positive
definiteness. Our main aim here is to give a complete description of algebraic condi tionally positive definite operators on inner product spaces; we do not assume that the
operators under consideration are bounded
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