# The conjugates and preconjugates of linear operators

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The preconjugate - Examples of admissible - Applications - Acknowledgements

Tipo de documento: Artículo - Article

Source: http://www.bdigital.unal.edu.co

## Teaser

MATEMATICAS THE CONJUGATES PURAS AND PRECONJUGATES OF LINEAR OPERATORS by KATHY an d S.
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A. With the aid of a systematic its conjugate complicated. X, THE De fin i t i o n . 1. FORBES cle Marylancl. ( Universiclacl 1. K. Y will dualor always adjoint spcce s.i T will will be the domain will be elements of be normed of T. X, Y, X Unless and Y respectively. Definition. for all x ~ Let In X. words Let implies = be its {y6Y continuous like to define = x A be a linear T ff(T) the unique F A subset operator v extension the preconjugate, in X if xx = 0 O. conjugate - F of X is total A mapping operator X to Y with.tY(A) mapping is continuous Y to X. on d(A)}, of v T, of T mapping- A to the whole of X to and dense In other Ty-is X.
We would Y.T should 3 be equal v to A or at least A x -: A y x xfi:f}(T) = Tyx if there and we define for all exists YEY T x = y. that the domain a linear the preconjugate, An element vv that Then x T, of X lies E we say for all defined y~.b(T), we require linear with ff(T) X to total spaces and Y-, Then in Y and is defined of T if there as follows. exi st...