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-vectors and boundedness

Jan Stochel, F. H. Szafraniec (1997)

Annales Polonici Mathematici

The following two questions as well as their relationship are studied: (i) Is a closed linear operator in a Banach space bounded if its -vectors coincide with analytic (or semianalytic) ones? (ii) When are the domains of two successive powers of the operator in question equal? The affirmative answer to the first question is established in case of paranormal operators. All these investigations are illustrated in the context of weighted shifts.

A characterization of reflexive spaces of operators

Janko Bračič, Lina Oliveira (2018)

Czechoslovak Mathematical Journal

We show that for a linear space of operators ( 1 , 2 ) the following assertions are equivalent. (i) is reflexive in the sense of Loginov-Shulman. (ii) There exists an order-preserving map Ψ = ( ψ 1 , ψ 2 ) on a bilattice Bil ( ) of subspaces determined by with P ψ 1 ( P , Q ) and Q ψ 2 ( P , Q ) for any pair ( P , Q ) Bil ( ) , and such that an operator T ( 1 , 2 ) lies in if and only if ψ 2 ( P , Q ) T ψ 1 ( P , Q ) = 0 for all ( P , Q ) Bil ( ) . This extends the Erdos-Power type characterization of weakly closed bimodules over a nest algebra to reflexive spaces.

A characterization of the essential spectrum and applications

Aref Jeribi (2002)

Bollettino dell'Unione Matematica Italiana

In this article the essential spectrum of closed, densely defined linear operators is characterized on a large class of spaces, which possess the Dunford-Pettis property or which isomorphic to one of the spaces L p Ω p > 1 . A practical...

A chart preserving the normal vector and extensions of normal derivatives in weighted function spaces

Katrin Schumacher (2009)

Czechoslovak Mathematical Journal

Given a domain Ω of class C k , 1 , k , we construct a chart that maps normals to the boundary of the half space to normals to the boundary of Ω in the sense that ( - x n ) α ( x ' , 0 ) = - N ( x ' ) and that still is of class C k , 1 . As an application we prove the existence of a continuous extension operator for all normal derivatives of order 0 to k on domains of class C k , 1 . The construction of this operator is performed in weighted function spaces where the weight function is taken from the class of Muckenhoupt weights.

A Class of Contractions in Hilbert Space and Applications

Nick Dungey (2007)

Bulletin of the Polish Academy of Sciences. Mathematics

We characterize the bounded linear operators T in Hilbert space which satisfy T = βI + (1-β)S where β ∈ (0,1) and S is a contraction. The characterizations include a quadratic form inequality, and a domination condition of the discrete semigroup ( T ) n = 1 , 2 , . . . by the continuous semigroup ( e - t ( I - T ) ) t 0 . Moreover, we give a stronger quadratic form inequality which ensures that s u p n T - T n + 1 : n = 1 , 2 , . . . < . The results apply to large classes of Markov operators on countable spaces or on locally compact groups.

A class of tridiagonal operators associated to some subshifts

Christian Hernández-Becerra, Benjamín A. Itzá-Ortiz (2016)

Open Mathematics

We consider a class of tridiagonal operators induced by not necessary pseudoergodic biinfinite sequences. Using only elementary techniques we prove that the numerical range of such operators is contained in the convex hull of the union of the numerical ranges of the operators corresponding to the constant biinfinite sequences; whilst the other inclusion is shown to hold when the constant sequences belong to the subshift generated by the given biinfinite sequence. Applying recent results by S. N....

A classification of projectors

Gustavo Corach, Alejandra Maestripieri, Demetrio Stojanoff (2005)

Banach Center Publications

A positive operator A and a closed subspace of a Hilbert space ℋ are called compatible if there exists a projector Q onto such that AQ = Q*A. Compatibility is shown to depend on the existence of certain decompositions of ℋ and the ranges of A and A 1 / 2 . It also depends on a certain angle between A() and the orthogonal of .

A commutant lifting theorem on analytic polyhedra

Calin Ambrozie, Jörg Eschmeier (2005)

Banach Center Publications

In this note a commutant lifting theorem for vector-valued functional Hilbert spaces over generalized analytic polyhedra in ℂⁿ is proved. Let T be the compression of the multiplication tuple M z to a *-invariant closed subspace of the underlying functional Hilbert space. Our main result characterizes those operators in the commutant of T which possess a lifting to a multiplier with Schur class symbol. As an application we obtain interpolation results of Nevanlinna-Pick and Carathéodory-Fejér type...

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