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2005•Journal of Xian Educational CollegeRequires access

Conjugate Linear Operators on Normed Spaces

Cao Huai-xin

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Abstract

Conjugate linear operators on normed spaces are discussed.Their continuity,boundedness and norm are studied.The relations between the space CCL(X,Y)of all continuous conjugate linear operators from X into Y and the space B(X,Y)of all continuous linear operators from X into Y are established.Furthermore,the W-dual space X~# of a complex normed space X is introduced.The W~# -dual operator:T~#:Y~#→X~# and W~×-dual operator:T~×:T~#→X~ˇ of a continuous conjugate linear operator:T:X→Y are defined.Finally,some important properties of them are also studied.

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Conjugate linear operators on normed spaces are discussed.Their continuity,boundedness and norm are studied.The relations between the space CCL(X,Y)of all continuous conjugate linear operators from X into Y and the space B(X,Y)of all continuous linear operators from X into Y are established.Furthermore,the W-dual space X~# of a complex normed space X is introduced.The W~# -dual operator:T~#:Y~#→X~# and W~×-dual operator:T~×:T~#→X~ˇ of a continuous conjugate linear operator:T:X→Y are defined.Finally,some important properties of them are also studied.

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Available abstract

Conjugate linear operators on normed spaces are discussed.Their continuity,boundedness and norm are studied.The relations between the space CCL(X,Y)of all continuous conjugate linear operators from X into Y and the space B(X,Y)of all continuous linear operators from X into Y are established.Furthermore,the W-dual space X~# of a complex normed space X is introduced.The W~# -dual operator:T~#:Y~#→X~# and W~×-dual operator:T~×:T~#→X~ˇ of a continuous conjugate linear operator:T:X→Y are defined.Finally,some important properties of them are also studied.

Key concepts: Dual norm, Normed vector space, Conjugate, Mathematics, Continuous linear operator, Norm (philosophy), Operator norm, Linear map

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