orthogonality in normed spaces
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2019 ◽  
Vol 8 (3) ◽  
pp. 1
Author(s):  
PRASAD OJHA BHUWAN ◽  
MUNI BAJRACHARYA PRAKASH ◽  
◽  

2017 ◽  
Vol 531 ◽  
pp. 305-317 ◽  
Author(s):  
Jacek Chmieliński ◽  
Tomasz Stypuła ◽  
Paweł Wójcik

2013 ◽  
Vol 33 (5) ◽  
pp. 1387-1397 ◽  
Author(s):  
N.B. OKELO ◽  
J.O. AGURE ◽  
P.O. OLECHE

2010 ◽  
Vol 73 (12) ◽  
pp. 3821-3831 ◽  
Author(s):  
Blaž Mojškerc ◽  
Aleksej Turnšek

Filomat ◽  
2009 ◽  
Vol 23 (1) ◽  
pp. 21-41 ◽  
Author(s):  
A. Bachir ◽  
A. Segres

Introducing the concept of the normalized duality mapping on normed linear 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 convexity of these types of numerical ranges in normed algebras and linear spaces. We establish some Birkhoff-James orthogonality results in terms of the algebra 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. .


Author(s):  
A. Blanco ◽  
A. Turnšek

We show that every orthogonality-preserving linear map between normed spaces is a scalar multiple of an isometry. Using this result, we generalize Uhlhorn's version of Wigner's theorem on symmetry transformations to a wide class of Banach spaces.


1986 ◽  
Vol 33 (3) ◽  
pp. 449-455 ◽  
Author(s):  
J. R. Partington

Some properties which different definitions or orthogonality in a normed space can possess are considered. It is shown that orthogonality can be defined on any separable space with many of the properties possessed by the usual orthogonality in an inner-product space, but that the possession of a further property forces the space to be isomorphic to a Euclidean space.


1986 ◽  
Vol 16 (2) ◽  
pp. 279-304
Author(s):  
Kazuo Hashimoto ◽  
Gen Nakamura ◽  
Shinnosuke Oharu

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