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Algebraic isomorphisms and Jordan derivations of 𝒥-subspace lattice algebras

Fangyan Lu, Pengtong Li (2003)

Studia Mathematica

It is shown that every algebraic isomorphism between standard subalgebras of 𝒥-subspace lattice algebras is quasi-spatial and every Jordan derivation of standard subalgebras of 𝒥-subspace lattice algebras is an additive derivation. Also, it is proved that every finite rank operator in a 𝒥-subspace lattice algebra can be written as a finite sum of rank one operators each belonging to that algebra. As an additional result, a multiplicative bijection of a 𝒥-subspace lattice algebra onto an arbitrary...

Algebraic properties of Toeplitz operators on weighted Bergman spaces

Amila Appuhamy (2021)

Czechoslovak Mathematical Journal

We study algebraic properties of two Toeplitz operators on the weighted Bergman space on the unit disk with harmonic symbols. In particular the product property and commutative property are discussed. Further we apply our results to solve a compactness problem of the product of two Hankel operators on the weighted Bergman space on the unit bidisk.

Algebras of quotients with bounded evaluation of a normed semiprime algebra

M. Cabrera, Amir A. Mohammed (2003)

Studia Mathematica

We deal with the algebras consisting of the quotients that produce bounded evaluation on suitable ideals of the multiplication algebra of a normed semiprime algebra A. These algebras of quotients, which contain A, are subalgebras of the bounded algebras of quotients of A, and they have an algebra seminorm for which the relevant inclusions are continuous. We compute these algebras of quotients for some norm ideals on a Hilbert space H: 1) the algebras of quotients with bounded evaluation of the ideal...

Algebras of Toeplitz operators with oscillating symbols.

Albrecht Böttcher, Sergei M. Grudsky, Enrique Ramírez de Arellano (2004)

Revista Matemática Iberoamericana

This paper is devoted to Banach algebras generated by Toeplitz operators with strongly oscillating symbols, that is, with symbols of the form b[eia(x)] where b belongs to some algebra of functions on the unit circle and a is a fixed orientation-preserving homeomorphism of the real line onto itself. We prove the existence of certain interesting homomorphisms and establish conditions for the normal solvability, Fredholmness, and invertibility of operators in these algebras.

Almost everywhere convergence of generalized ergodic transforms for invertible power-bounded operators in L p

Christophe Cuny (2011)

Colloquium Mathematicae

We show that some results of Gaposhkin about a.e. convergence of series associated to a unitary operator U acting on L²(X,Σ,μ) (μ is a σ-finite measure) may be extended to the case where U is an invertible power-bounded operator acting on L p ( X , Σ , μ ) , p > 1. The proofs make use of the spectral integration initiated by Berkson-Gillespie and, more specifically, of recent results of the author.

Almost exactness in normed spaces II

Robin Harte, Мostafa Мbekhta (1996)

Studia Mathematica

In the normed space of bounded operators between a pair of normed spaces, the set of operators which are "bounded below" forms the interior of the set of one-one operators. This note is concerned with the extension of this observation to certain spaces of pairs of operators.

Almost Weakly Compact Operators

Ioana Ghenciu, Paul Lewis (2006)

Bulletin of the Polish Academy of Sciences. Mathematics

Dunford-Pettis type properties are studied in individual Banach spaces as well as in spaces of operators. Bibasic sequences are used to characterize Banach spaces which fail to have the Dunford-Pettis property. The question of whether a space of operators has a Dunford-Pettis property when the dual of the domain and the codomain have the respective property is studied. The notion of an almost weakly compact operator plays a consistent and important role in this study.

Alternative characterisations of Lorentz-Karamata spaces

David Eric Edmunds, Bohumír Opic (2008)

Czechoslovak Mathematical Journal

We present new formulae providing equivalent quasi-norms on Lorentz-Karamata spaces. Our results are based on properties of certain averaging operators on the cone of non-negative and non-increasing functions in convenient weighted Lebesgue spaces. We also illustrate connections between our results and mapping properties of such classical operators as the fractional maximal operator and the Riesz potential (and their variants) on the Lorentz-Karamata spaces.

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