Some Results on Frame Operators in 2-Hilbert Spaces
DOI:
https://doi.org/10.5269/bspm.82362Abstract
We investigate operator-theoretic aspects of frames in 2-Hilbert spaces. Frames associated with a
fixed vector are considered, and corresponding frame operators are introduced. The notions of zero operators,
equality of operators, and adjoint operators are extended from Hilbert spaces to the 2-Hilbert setting. It is
shown that frame operators are linear, bounded, positive, self-adjoint, and invertible in the 2-Hilbert sense.
For finite-dimensional 2-Hilbert spaces, matrix representations of frame operators are obtained. Canonical
dual frames and reconstruction formulas are also established.
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