Skew-Symmetric Operators and Isometries on a Real Banach Space with a Hyperorthogonal Basis

Legǐsa, Peter

doi:10.1007/978-3-0348-7698-8_16

Peter Legǐsa³

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 17))

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Abstract

A Schauder basis {e_i; i ε N} of a Banach space X is hyperorthogonal if

$$\left\| {\sum {{a_{\text{i}}}{e_{\text{i}}}} } \right\| = \left\| {\sum {\left| {{a_{\text{i}}}} \right|\left| {{e_{\text{i}}}} \right|} } \right\|$$

for arbitrary scalars a_i (i ε N). In this case the following is true (see [6]):

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Authors and Affiliations

Department of Mathematics, Institute of Mathematics, Physics and Mechanics, Jadranska 19, 61000, Ljubljana, Yugoslavia
Peter Legǐsa

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Peter Legǐsa
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Editors and Affiliations

Department of Mathematics, INCREST, Bd. Păcii 220, 79622, Bucharest, Romania
R. G. Douglas , C. M. Pearcy , B. Sz.-Nagy , F.-H. Vasilescu & Dan Voiculescu , , , &

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Legǐsa, P. (1986). Skew-Symmetric Operators and Isometries on a Real Banach Space with a Hyperorthogonal Basis. In: Douglas, R.G., Pearcy, C.M., Sz.-Nagy, B., Vasilescu, FH., Voiculescu, D., Arsene, G. (eds) Advances in Invariant Subspaces and Other Results of Operator Theory. Operator Theory: Advances and Applications, vol 17. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7698-8_16

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DOI: https://doi.org/10.1007/978-3-0348-7698-8_16
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-7700-8
Online ISBN: 978-3-0348-7698-8
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