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In this paper we analyse a definition of a product of Banach spaces that is naturally associated by duality with a space of operators that can be considered as a generalization of the notion of space of multiplication operators. This dual relation allows to understand several constructions coming from different fields of functional analysis that can be seen as instances of the abstract one when a particular product is considered. Some relevant examples and applications are shown, regarding pointwise...

Projections, extendability of operators and the Gâteaux derivative of the norm.

Gajek, L., Jachymski, J., Zagrodny, D. (1995)

Journal of Applied Analysis

Projections, skewness and related constants in real normed spaces.

Baronti, Marco, Papini, Pier Luigi (1992)

Mathematica Pannonica

Proper subspaces and compatibility

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

Studia Mathematica

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. Furthermore,...

Pseudo-Monotone Operators in Banach Spaces and Nonlinear Elliptic Equations.

Bui An Ton (1971)

Mathematische Zeitschrift

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