|
In mathematics, multipliers and centralizers are algebraic objects in the study of Banach spaces. They are used, for example, in generalizations of the Banach-Stone theorem. ==Definitions== Let (''X'', ||·||) be a Banach space over a field K (either the real or complex numbers), and let Ext(''X'') be the set of extreme points of the closed unit ball of the continuous dual space ''X''∗. A continuous linear operator ''T'' : ''X'' → ''X'' is said to be a multiplier if every point ''p'' in Ext(''X'') is an eigenvector for the adjoint operator ''T''∗ : ''X''∗ → ''X''∗. That is, there exists a function ''a''''T'' : Ext(''X'') → K such that : making the eigenvalue corresponding to ''p''. Given two multipliers ''S'' and ''T'' on ''X'', ''S'' is said to be an adjoint for ''T'' if : i.e. ''a''''S'' agrees with ''a''''T'' in the real case, and with the complex conjugate of ''a''''T'' in the complex case. The centralizer of ''X'', denoted ''Z''(''X''), is the set of all multipliers on ''X'' for which an adjoint exists. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Multipliers and centralizers (Banach spaces)」の詳細全文を読む スポンサード リンク
|