Uniformly invariant normed spaces

In this work, we introduce the concepts of compactly invariant and uniformly invariant. Also we define sometimes C-invariant closed subspaces and then prove every m-dimensional normed space with m > 1 has a nontrivial sometimes C-invariant closed subspace. Sequentially C-invariant closed subspace...

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Bibliographic Details
Published inBibechana Vol. 10; pp. 31 - 33
Main Authors Forouzanfar, AM, Khorshidvandpour, S, Bahmani, Z
Format Journal Article
LanguageEnglish
Published Department of Physics, Mahendra Morang Adarsh Multiple Campus, Tribhuvan University 31.10.2013
Subjects
Completely invariant space
Positive operator
Uniformly invariant space
Unitary space
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Summary:In this work, we introduce the concepts of compactly invariant and uniformly invariant. Also we define sometimes C-invariant closed subspaces and then prove every m-dimensional normed space with m > 1 has a nontrivial sometimes C-invariant closed subspace. Sequentially C-invariant closed subspaces are also introduced. Next, An open problem on the connection between compactly invariant and uniformly invariant normed spaces has been posed. Finally, we prove a theorem on the existence of a positive operator on a strict uniformly invariant Hilbert space. DOI: http://dx.doi.org/10.3126/bibechana.v10i0.7555 BIBECHANA 10 (2014) 31-33
ISSN:2091-0762
2382-5340
DOI:10.3126/bibechana.v10i0.7555