Formulas for the operator norm and the extension of a linear functional on a linear subspace of a Hilbert Space
Formulas for the operator norm and the extension of a linear functional on a linear subspace of a Hilbert Space
In this paper, formulas are given both for the operator norm and for the extension of a linear functionaldefined on a linear subspace of a Hilbert space and the results are illustrated with examples.
Keywords:
Linear functional, Cauchy-Schwarz inequality, norm, operator norm, Hilbert spaces, Hahn-Banach theorem, Riesz representation theorem, orthogonal vectors orthogonal decomposition,
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- 1) B. Beauzam\i, \emph{Introduction to Banach Spaces and Their Geometry}, North Holland Publishing Com. Inc., Amsterdam, 1982.6)
- 2) B\'{e}la Bollob\'{a}s, \emph{Linear Anaysis}, Cambridge Univ. Press, Cambridge, 1990.
- 3) L. Narici, E. Beckenstein, \emph{The Hahn-Banach theorem: the lifes and times}, Topology and its Applications 77(1997), 193-211
- ISSN: 2687-6531
- Yayın Aralığı: Yılda 2 Sayı
- Başlangıç: 2019
- Yayıncı: Nihat AKGÜNEŞ
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