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On order structure and operators in L ∞(μ)

Irina Krasikova, Miguel Martín, Javier Merí, Vladimir Mykhaylyuk, Mikhail Popov (2009)

Open Mathematics

It is known that there is a continuous linear functional on L ∞ which is not narrow. On the other hand, every order-to-norm continuous AM-compact operator from L ∞(μ) to a Banach space is narrow. We study order-to-norm continuous operators acting from L ∞(μ) with a finite atomless measure μ to a Banach space. One of our main results asserts that every order-to-norm continuous operator from L ∞(μ) to c 0(Γ) is narrow while not every such an operator is AM-compact.

On partial isometries in C*-algebras

M. Laura Arias, Mostafa Mbekhta (2011)

Studia Mathematica

We study similarity to partial isometries in C*-algebras as well as their relationship with generalized inverses. Most of the results extend some recent results regarding partial isometries on Hilbert spaces. Moreover, we describe partial isometries by means of interpolation polynomials.

On product of projections

Mohammad Sal Moslehian (2004)

Archivum Mathematicum

An operator with infinite dimensional kernel is positive iff it is a positive scalar times a certain product of three projections.

On products of some Toeplitz operators on polyanalytic Fock spaces

Irène Casseli (2020)

Czechoslovak Mathematical Journal

The purpose of this paper is to study the Sarason’s problem on Fock spaces of polyanalytic functions. Namely, given two polyanalytic symbols f and g , we establish a necessary and sufficient condition for the boundedness of some Toeplitz products T f T g ¯ subjected to certain restriction on f and g . We also characterize this property in terms of the Berezin transform.

On Pták’s generalization of Hankel operators

Carmen H. Mancera, Pedro José Paúl (2001)

Czechoslovak Mathematical Journal

In 1997 Pták defined generalized Hankel operators as follows: Given two contractions T 1 ∈ ℬ ( ℋ 1 ) and T 2 ∈ ℬ ( ℋ 2 ) , an operator X ℋ 1 → ℋ 2 is said to be a generalized Hankel operator if T 2 X = X T 1 * and X satisfies a boundedness condition that depends on the unitary parts of the minimal isometric dilations of T 1 and T 2 . 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 quasi-compactness of operator nets on Banach spaces

Eduard Yu. Emel'yanov (2011)

Studia Mathematica

The paper introduces a notion of quasi-compact operator net on a Banach space. It is proved that quasi-compactness of a uniform Lotz-Räbiger net ( T λ ) λ is equivalent to quasi-compactness of some operator T λ . We prove that strong convergence of a quasi-compact uniform Lotz-Räbiger net implies uniform convergence to a finite-rank projection. Precompactness of operator nets is also investigated.

On Quasi-Normality of Two-Sided Multiplication

Amouch, M. (2009)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 47B47, 47B10, 47A30.In this note, we characterize quasi-normality of two-sided multiplication, restricted to a norm ideal and we extend this result, to an important class which contains all quasi-normal operators. Also we give some applications of this result.

Currently displaying 181 – 200 of 491