ORTHOGONALITY AND SMOOTH POINTS IN C(K) AND Cb( )

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dc.contributor.author D.J. Keˇcki´
dc.date.accessioned 2013-06-26T09:23:38Z
dc.date.available 2013-06-26T09:23:38Z
dc.date.issued 2013-06-26
dc.identifier.uri http://repository.enu.kz/handle/data/10784
dc.description.abstract For the usual norm on spaces C(K) and Cb( ) of all continuous functions on a compact Hausdorff space K (all bounded continuous functions on a locally compact Hausdorff space ), the following equalities are proved: lim t!0+ ||f + tg||C(K) − ||f||C(K) t = max x2{z | |f(z)|=||f||} Re(e−i arg f(x)g(x)). and lim t!0+ ||f + tg||Cb( ) − ||f||Cb( ) t = inf >0 sup x2{z | |f(z)| ||f||− } Re(e−i arg f(x)g(x)). These equalities are used to characterize the orthogonality in the sense of James (Birkhoff) in spaces C(K) and Cb( ) as well as to give necessary and sufficient conditions for a point on the unit sphere to be a smooth point. ru_RU
dc.language.iso en ru_RU
dc.subject orthogonality in the sense of James ru_RU
dc.subject Gateaux derivative ru_RU
dc.subject smooth points ru_RU
dc.title ORTHOGONALITY AND SMOOTH POINTS IN C(K) AND Cb( ) ru_RU
dc.type Article ru_RU


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