On $J$-frames related to maximal definite subspaces

Alan Kamuda; Sergiusz Kużel

On $J$-frames related to maximal definite subspaces

Functional Analysis 2018-01-09 v3

Authors: Alan Kamuda , Sergiusz Kużel

Abstract

A definition of frames in Krein spaces is proposed which extends the concept of $J$ -frames defined by J.I. Giribet et al., J. Math. Anal. Appl. ${\textbf{393}}$ (2012), 122-137. The principal difference consists in the fact that a $J$ -frame is related to maximal definite subspaces $\mathcal{M}_\pm$ which are not assumed to be uniformly definite. The latter allows one to extend the collection of $J$ -frames. In particular, some complete $J$ -orthogonal sequences and $J$ -orthogonal Schauder bases can be interpreted as $J$ -frames.

Keywords

frame theory topological spaces

Cite

@article{arxiv.1712.08050,
  title  = {On $J$-frames related to maximal definite subspaces},
  author = {Alan Kamuda and Sergiusz Kużel},
  journal= {arXiv preprint arXiv:1712.08050},
  year   = {2018}
}

Comments

15 pages.arXiv admin note: text overlap with arXiv:1703.03665 by other authors

On $J$-frames related to maximal definite subspaces

Abstract

Keywords

Cite

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