On a fixed-point theorem of Cellina
In questa nota mostriamo come un teorema di esistenza per funzionali lineari porti un nuovo teorema di punto fisso che generalizza un teorema di punto fisso di Cellina.
On a general bidimensional extrapolation problem
Several generalized moment problems in two dimensions are particular cases of the general problem of giving conditions that ensure that two isometries, with domains and ranges contained in the same Hilbert space, have commutative unitary extensions to a space that contains the given one. Some results concerning this problem are presented and applied to the extension of functions of positive type.
On multi-contractions having a regular dilation
Commuting multi-contractions of class and having a regular isometric dilation are studied. We prove that a polydisc contraction of class is the restriction of a backwards multi-shift to an invariant subspace, extending a particular case of a result by R. E. Curto and F.-H. Vasilescu. A new condition on a commuting multi-operator, which is equivalent to the existence of a regular isometric dilation and improves a recent result of A. Olofsson, is obtained as a consequence.
On Davis-Kahan-weinberger Extension Theorem
On decomposition of pairs of commuting isometries
A review of known decompositions of pairs of isometries is given. A new, finer decomposition and its properties are presented.
On essential selfadjointness of the Weyl quantized relativistic Hamiltonian.
On generalized localizability
On nonstationary periodically correlated processes in complete correlated actions.
On operators with unitary ϱ-dilations
We show a polynomially boundend operator T is similar to a unitary operator if there is a singular unitary operator W and an injection X such that XT = WX. If, in addition, T is of class , then T itself is unitary.
On problems concerning extension of linear operations on linear spaces
On problems concerning uniqueness of the extension of linear operations on linear spaces
On Pták’s generalization of Hankel operators
In 1997 Pták defined generalized Hankel operators as follows: Given two contractions and , an operator is said to be a generalized Hankel operator if and satisfies a boundedness condition that depends on the unitary parts of the minimal isometric dilations of and . This approach, call it (P), contrasts with a previous one developed by Pták and Vrbová in 1988, call it (PV), based on the existence of a previously defined generalized Toeplitz operator. There seemed to be a strong but somewhat...
On regular extensions of operator systems.
On some constructions of new triangular norms.
We discuss the properties of two types of construction of a new t-norm from a given t-norm proposed recently by B. Demant, namely the dilatation and the contraction. In general, the dilatation of a t-norm is an ordinal sum t-norm and the continuity of the outgoing t-norm is preserved. On the other hand, the contraction may violate the continuity as well as the non-continuity of the outgoing t-norm. Several examples are given.
On some dilation theorems for positive definite operator valued functions
The aim of this paper is to prove dilation theorems for operators from a linear complex space to its Z-anti-dual space. The main result is that a bounded positive definite function from a *-semigroup Γ into the space of all continuous linear maps from a topological vector space X to its Z-anti-dual can be dilated to a *-representation of Γ on a Z-Loynes space. There is also an algebraic counterpart of this result.
On strictly singular operators
On the Davis-Kahan-Weinberger Solution of the Norm-Preserving Dilation Problem.
On the defect spectrum of an extension of a Banach space operator
Let be an operator acting on a Banach space . We show that between extensions of to some Banach space which do not increase the defect spectrum (or the spectrum) it is possible to find an extension with the minimal possible defect spectrum.
On the intertwinings of regular dilations
The aim of this paper is to find conditions that assure the existence of the commutant lifting theorem for commuting pairs of contractions (briefly, bicontractions) having (*-)regular dilations. It is known that in such generality, a commutant lifting theorem fails to be true. A positive answer is given for contractive intertwinings which doubly intertwine one of the components. We also show that it is possible to drop the doubly intertwining property for one of the components in some special cases,...
On the point spectrum of self-adjoint extensions.