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.

In this paper, we generalize the definition of fuzzy inner product space that is introduced by Lorena Popa and Lavinia Sida on a complex linear space. Certain properties generalized function are shown. Furthermore, prove produces Nadaban-Dzitac norm. Finally, concept orthogonality given some its proven.

In quantum mechanics, physical states are represented by rays in Hilbert space $\mathcal{H}$, which is a vector imbued an inner product $\ensuremath{\langle}\phantom{\rule{0.16em}{0ex}}|\phantom{\rule{0.16em}{0ex}}\ensuremath{\rangle}$, whose meaning arises as the overlap $\ensuremath{\langle}\ensuremath{\phi}|\ensuremath{\psi}\ensuremath{\rangle}$ for $|\ensuremath{\psi}\ensuremath{\rangle}$ p...

In this paper, for the first time, notion of multi complex numbers and number valued inner product is introduced in linear (vector) space. Starting from definition, some basic properties spaces are studied along with examples. Multi parallelogram law polarization identity established

Abstract We say that a smooth normed space X has property (SL) , if every mapping $$f:X \rightarrow X$$ f : X → preserving the semi-inner product on is linear. It well known Hilbert and same true for finite-dimensional space. In this pa...

This paper presents new results related to Bombieri’s generalization of Bessel’s inequality in a semi-inner product space induced by positive semidefinite operator A. Specifically, we establish inequalities that generalize the classical Bessel and extend previous this area. Furthermore, our findings have applications study operators on inner spaces, also known as semi-Hilbert contribute deeper ...

This paper is an investigation of $L$-dual frames with respect to a function-valued inner product, the so called $L$-bracket product on $L^{2}(G)$, where G is a locally compact abelian group with a uniform lattice $L$. We show that several well known theorems for dual frames and dual Riesz bases in a Hilbert space remain valid for $L$-dual frames and $L$-dual Riesz bases in $L^{2}(G)$.