Displaying similar documents to “Some properties of prereflexive subspaces of operators.”

Ultraweakly compact operators and dual spaces

Teresa Alvarez (2004)

Bollettino dell'Unione Matematica Italiana

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In this paper, the class of all bounded ultraweakly compact operators in Banach spaces is introduced and characterised in terms of their first and second conjugates. We analize the relationship between an ultraweakly compact operator and its conjugate. Examples of operators belonging to this class are exhibited. We also investigate the connection between ultraweak compactness of T ∈ L ⁢ X , Y and minimal subspaces of Y ′ and we present a result of factorisation for ultraweakly compact operators. ...

Proper subspaces and compatibility

Esteban Andruchow, Eduardo Chiumiento, María Eugenia Di Iorio y Lucero (2015)

Studia Mathematica

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Let 𝓔 be a Banach space contained in a Hilbert space 𝓛. Assume that the inclusion is continuous with dense range. Following the terminology of Gohberg and Zambickiĭ, we say that a bounded operator on 𝓔 is a proper operator if it admits an adjoint with respect to the inner product of 𝓛. A proper operator which is self-adjoint with respect to the inner product of 𝓛 is called symmetrizable. By a proper subspace 𝓢 we mean a closed subspace of 𝓔 which is the range of a proper projection....

Quotients of Banach Spaces with the Daugavet Property

Vladimir Kadets, Varvara Shepelska, Dirk Werner (2008)

Bulletin of the Polish Academy of Sciences. Mathematics

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We consider a general concept of Daugavet property with respect to a norming subspace. This concept covers both the usual Daugavet property and its weak* analogue. We introduce and study analogues of narrow operators and rich subspaces in this general setting and apply the results to show that a quotient of L₁[0,1] by an ℓ₁-subspace need not have the Daugavet property. The latter answers in the negative a question posed to us by A. Pełczyński.