| Autor: |
Giribet, Juan Ignacio, Langer, Matthias, Leben, Leslie, Maestripieri, Alejandra, Pería, Francisco Martínez, Trunk, Carsten |
| Rok vydání: |
2017 |
| Předmět: |
|
| Zdroj: |
Opuscula Math. 38 (2018), 623-649 |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.7494/OpMath.2018.38.5.623 |
| Popis: |
A $J$-frame is a frame $\mathcal{F}$ for a Krein space $(\mathcal{H}, [\, , \,])$ which is compatible with the indefinite inner product $[\, , \, ]$ in the sense that it induces an indefinite reconstruction formula that resembles those produced by orthonormal bases in $\mathcal{H}$. With every $J$-frame the so-called $J$-frame operator is associated, which is a self-adjoint operator in the Krein space $\mathcal{H}$. The $J$-frame operator plays an essential role in the indefinite reconstruction formula. In this paper we characterize the class of $J$-frame operators in a Krein space by a $2\times 2$ block operator representation. The $J$-frame bounds of $\mathcal{F}$ are then recovered as the suprema and infima of the numerical ranges of some uniformly positive operators which are build from the entries of the $2\times 2$ block representation. Moreover, this $2\times 2$ block representation is utilized to obtain enclosures for the spectrum of $J$-frame operators, which finally leads to the construction of a square root. This square root allows a complete description of all $J$-frames associated with a given $J$-frame operator. |
| Databáze: |
arXiv |
| Externí odkaz: |
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