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On spectral continuity of positive elements

S. Mouton (2006)

Studia Mathematica

Let x be a positive element of an ordered Banach algebra. We prove a relationship between the spectra of x and of certain positive elements y for which either xy ≤ yx or yx ≤ xy. Furthermore, we show that the spectral radius is continuous at x, considered as an element of the set of all positive elements y ≥ x such that either xy ≤ yx or yx ≤ xy. We also show that the property ϱ(x + y) ≤ ϱ(x) + ϱ(y) of the spectral radius ϱ can be obtained for positive elements y which satisfy at least one of the...

On the class of order almost L-weakly compact operators

Kamal El Fahri, Hassan Khabaoui, Jawad Hmichane (2022)

Commentationes Mathematicae Universitatis Carolinae

We introduce a new class of operators that generalizes L-weakly compact operators, which we call order almost L-weakly compact. We give some characterizations of this class and we show that this class of operators satisfies the domination problem.

On the dependence of the orthogonal projector on deformations of the scalar product

Zbigniew Pasternak-Winiarski (1998)

Studia Mathematica

We consider scalar products on a given Hilbert space parametrized by bounded positive and invertible operators defined on this space, and orthogonal projectors onto a fixed closed subspace of the initial Hilbert space corresponding to these scalar products. We show that the projector is an analytic function of the scalar product, we give the explicit formula for its Taylor expansion, and we prove some algebraic formulas for projectors.

On the equality between some classes of operators on Banach lattices

Belmesnaoui Aqzzouz, Aziz Elbour, Mohammed Moussa (2012)

Mathematica Bohemica

We establish some sufficient conditions under which the subspaces of Dunford-Pettis operators, of M-weakly compact operators, of L-weakly compact operators, of weakly compact operators, of semi-compact operators and of compact operators coincide and we give some consequences.

On the positivity of semigroups of operators

Roland Lemmert, Peter Volkmann (1998)

Commentationes Mathematicae Universitatis Carolinae

In a Banach space E , let U ( t ) ( t > 0 ) be a C 0 -semigroup with generating operator A . For a cone K ⊆ E ...

On the structure of positive maps between matrix algebras

Władysław A. Majewski, Marcin Marciniak (2007)

Banach Center Publications

The structure of the set of positive unital maps between M₂(ℂ) and Mₙ(ℂ) (n ≥ 3) is investigated. We proceed with the study of the "quantized" Choi matrix thus extending the methods of our previous paper [MM2]. In particular, we examine the quantized version of Størmer's extremality condition. Maps fulfilling this condition are characterized. To illustrate our approach, a careful analysis of Tang's maps is given.

On uniformly smoothing stochastic operators

Wojciech Bartoszek (1995)

Commentationes Mathematicae Universitatis Carolinae

We show that a stochastic operator acting on the Banach lattice L 1 ( m ) of all m -integrable functions on ( X , 𝒜 ) is quasi-compact if and only if it is uniformly smoothing (see the definition below).

Once more on positive commutators

Roman Drnovšek (2012)

Studia Mathematica

Let A and B be bounded operators on a Banach lattice E such that the commutator C = AB - BA and the product BA are positive operators. If the product AB is a power-compact operator, then C is a quasi-nilpotent operator having a triangularizing chain of closed ideals of E. This answers an open question posed by Bračič et al. [Positivity 14 (2010)], where the study of positive commutators of positive operators was initiated.

Currently displaying 61 – 80 of 139