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Some Results on Frame Operators in 2-Hilbert Spaces
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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.
Sociedade Paranaense de Matemática
Title: Some Results on Frame Operators in 2-Hilbert Spaces
Description:
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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