# Representations of the weak Calkin algebra

Gonzàlez, Manuel (1994) Representations of the weak Calkin algebra. Accademia Peloritana dei Pericolanti, Classe di Scienze FF. MM. NN., LXXII. pp. 153-169.

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## Abstract

Let denote the space of all continuous linear operators in a Banch space . For every the operator is defined by . The map induces a representation of the weak Calkin algebra , rhe quotient of by the ideal of all weakly compact operators on , in the algebra .
Here we give a survey of the properties of the map R: if it has dense range or closed range, if it is surjective, etc., and describe some applications. We present examples showing that the properties of R can be very different on different spaces E. In some cases the only compact operator in the image of R is the null operator, in the other cases R is surjective, and in the case of , where J is James' space, we have that and the image of R is the class of lattice regular operators on . Among the applications, we show how to obtain examples of tauberian operators T so that is not tauberian, and operators such that R(T) is invertible in but T fails to be invertible modulo W(E).

Item Type: Article M.U.S. - Miscellanea > Atti Accademia Peloritana > Classe di Scienze Fisiche, Matematiche e Naturali > 1994M.U.S. - Miscellanea > Atti Accademia Peloritana > Classe di Scienze Medico-Biologiche > 1994M.U.S. - Miscellanea > Atti Accademia Peloritana > Classe di Scienze Giuridiche, Economiche e Politiche > 1994M.U.S. - Miscellanea > Atti Accademia Peloritana > Classe di Lettere, Filosofia e belle Arti > 1994 UNSPECIFIED Dr A F 19 Sep 2012 13:42 20 Sep 2012 10:14 http://cab.unime.it/mus/id/eprint/680