Zenon Jan Jabłoński

Hyperexpansive composition operators

The notion of a completely hyperexpansive operator has been introduced in [ 2 ] by Athavale. In this paper bounded and unbounded hyperexpansive composition operators are investigated. A unique semispectral measure is associated with a bounded completely hyperexpansive composition operator. Examples of bounded and unbounded densely defined

A hyponormal weighted shift on a directed tree whose square has trivial domain

2

Complete hyperexpansivity, subnormality and inverted boundedness conditions

-isometric (completely hyperexpansive,

On unbounded composition operators in L^2-spaces

2

UNBOUNDED 2-HYPEREXPANSIVE OPERATORS

-hyperexpansive) composition operators with invariant domains are given.

Subnormal Weighted Shifts on Directed Trees and Composition Operators in 2-Spaces with Nondensely Defined Powers

It is proved that, up to isomorphism, there are only two directed trees that admit a hyponormal weighted shift with nonzero weights whose square has trivial domain. These are precisely those enumerable directed trees, one with root, the other without, whose every vertex has enumerable set of successors.

Unbounded weighted composition operators in l²-spaces

Athavale introduced in [3] the notion of a completely hyperexpansive operator. In this paper some results concerning powers of completely (alternatingly) hyperexpansive operators (not necessarily bounded) are extended tok-hyperexpansive ones. A semispectral measure is associated with a subnormal contraction as well as with a completely hyperexpansive operator, and an operator version of the Levy-Khinchin representation is obtained. Passing to the Naimark dilation of the semispectral measure, such an operator is related to a positive contraction in a natural way. New characterizations of a completely hyperexpansive operator and a subnormal contraction are given. The power bounded completely hyperexpansive operators are characterized. All these are illustrated using weighted shifts.

HYPEREXPANSIVE OPERATOR VALUED UNILATERAL WEIGHTED SHIFTS

Fundamental properties of unbounded composition operators in

Moment problem with contractive solutions: the regular case

L^2