In the present paper, we investigate a connection between two fuzzy inner product one of which arises from Felbin's fuzzy norm and the other is based on Bag and Samanta's fuzzy norm. Also we show that, considering a fuzzy inner product space, how one can construct another kind of fuzzy inner product on this space.

we define a new function-valued inner product on l2(g), called ?-bracket product, where g is a locally compact abelian group and ? is a topological isomorphism on g. we investigate the notion of ?-orthogonality, bessel's inequality and ?-orthonormal bases with respect to this inner product on l2(g).

We introduce and  study  fuzzy (co-)inner product and fuzzy(co-)norm of hyperspaces. In this regard by considering  the notionof hyperspaces, as a generalization of vector spaces, first we willintroduce the notion of fuzzy (co-)inner product in hyperspaces and will apply it to formulate the notions offuzzy (co-)norm and fuzzy (co-)orthogonality  in hyperspaces. Inparticular, we will prove that ...

1. Signature Characters and the Jantzen Filtration 1 1.1. Jantzen Filtrations on Standard Modules 1 1.2. Hermitian Duals 3 1.3. Rationality of Signature Characters 5 1.4. Asymptotic Signatures 7 1.5. Isotypic Signature Characters 8 2. The Dunkl Weight Function 10 2.1. The Gaussian Inner Product 10 2.2. Weight Function 10 2.3. Analytic Continuation on the Regular Locus 20 2.4. Extension to Distr...

We define a new function-valued inner product on L2(G), called ?-bracket product, where G is a locally compact abelian group and ? is a topological isomorphism on G. We investigate the notion of ?-orthogonality, Bessel's Inequality and ?-orthonormal bases with respect to this inner product on L2(G).

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.