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Volume 1 (2016)
Issue 1
Issue 2
Chmielinski, J. (2016). Operators reversing orthogonality in normed spaces.
Advances in Operator Theory
, 1(1), 8-14. doi: 10.22034/aot.1610.1021
Jacek Chmielinski. "Operators reversing orthogonality in normed spaces".
Advances in Operator Theory
, 1, 1, 2016, 8-14. doi: 10.22034/aot.1610.1021
Chmielinski, J. (2016). 'Operators reversing orthogonality in normed spaces',
Advances in Operator Theory
, 1(1), pp. 8-14. doi: 10.22034/aot.1610.1021
Chmielinski, J. Operators reversing orthogonality in normed spaces.
Advances in Operator Theory
, 2016; 1(1): 8-14. doi: 10.22034/aot.1610.1021
Operators reversing orthogonality in normed spaces
Article 2
,
Volume 1, Issue 1
, Autumn 2016
, Page
8-14
PDF (259 K)
Document Type: Original Article
DOI:
10.22034/aot.1610.1021
Author
Jacek Chmielinski
Pedagogical University of Cracow
Abstract
We consider linear operators $T\colon X\to X$ on a normed space $X$ which reverse orthogonality, i.e., satisfy the condition
$$
x\bot y\quad \Longrightarrow\quad Ty\bot Tx,\qquad x,y\in X,
$$
where $\bot$ stands for Birkhoff orthogonality.
Keywords
Birkhoff orthogonality
;
orthogonality preserving mappings
;
orthogonality reversing map-pings
;
linear similarities
;
characterizations of inner product spaces
Main Subjects
15Axx: Basic linear algebra
;
46Bxx: Normed linear spaces and Banach spaces; Banach lattices
;
46Cxx: Inner product spaces and their generalizations, Hilbert spaces
;
47Axx: General theory of linear operators
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