Fredholm Nature of Orbital Frame Operators in Hilbert Spaces

A linear operator T on a Hilbert space H is said to be orbital frame if there exists a vector x ∈ H such that orb(T, f) constitutes a frame. This paper presents a novel examination of frames in the context of Hilbert space H, showing that orbital frame operators must be Fredholm. In particular, if an orbital frame operator T either has a dense range or is one-to-one then it is an invertible. MSC2020 Classification: 46B15 , 47B02