Partial inner product spaces. II. Operators

$C^{*}$-semi-inner product spaces

In this paper, we introduce a generalization of Hilbert $C^*$-modules which are pre-Finsler modules, namely, $C^{*}$-semi-inner product spaces. Some properties and results of such spaces are investigated, specially the orthogonality in these spaces will be considered. We then study bounded linear operators on $C^{*}$-semi-inner product spaces.

Partial Inner Product Spaces: Some Categorical Aspects

Frames in 2-inner Product Spaces

In this paper, we introduce the notion of a frame in a 2- inner product space and give some characterizations. These frames can be considered as a usual frame in a Hilbert space, so they share many useful properties with frames.

Atomic Systems in 2-inner Product Spaces

In this paper, we introduce the concept of family of local atoms in a 2-inner product space and then this concept is generalized to an atomic system. Besides, a characterization of an atomic system lead to obtain a new frame. Actually this frame is a generalization of previous works.

Canonical matrices of isometric operators on indefinite inner product spaces

We give canonical matrices of a pair (A,B) consisting of a nondegenerate form B and a linear operator A satisfying B(Ax,Ay) = B(x, y) on a vector space over F in the following cases: • F is an algebraically closed field of characteristic different from 2 or a real closed field, and B is symmetric or skew-symmetric; • F is an algebraically closed field of characteristic 0 or the skew field of qu...