Some Results on Frame Operators in 2-Hilbert Spaces

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.