Numerical range and orthogonality in normed spaces | Zendy

A‎. ‎Bachir | Zendy; A. Segres | Zendy

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Numerical range and orthogonality in normed spaces

Author(s) -

A‎. ‎Bachir,

A. Segres

Publication year - 2009

Publication title -

filomat

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.449

H-Index - 34

eISSN - 2406-0933

pISSN - 0354-5180

DOI - 10.2298/fil0901021b

Subject(s) - numerical range , mathematics , normed algebra , orthogonality , normed vector space , range (aeronautics) , convexity , duality (order theory) , linear map , algebra over a field , space (punctuation) , operator (biology) , pure mathematics , discrete mathematics , division algebra , algebra representation , geometry , linguistics , philosophy , materials science , biochemistry , chemistry , repressor , gene , transcription factor , financial economics , economics , composite material

Introducing the concept of the normalized duality mapping on normed lin- ear space and normed algebra, we extend the usual definitions of the numerical range from one operator to two operators. In this note we study the convex- ity of these types of numerical ranges in normed algebras and linear spaces. We establish some Birkho-James orthogonality results in terms of the alge- bra numerical range V (T)A which generalize those given by J.P. William and J.P. Stamplfli. Finally, we give a positive answer of the Mathieu's question.

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