$C^{*}$-semi-inner product spaces
Authors
Abstract:
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.
similar resources
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.
full textAtomic 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.
full textNumerical Range of Two Operators in Semi-Inner Product Spaces
and Applied Analysis 3 was studied by Verma 14 . He defined the numerical range VL T of a nonlinear operator T , as VL T : { Tx, x [ Tx − Ty, x − y ‖x‖ ∥x − y∥2 : x, y ∈ D T , x / y } . 1.3 He used this concept to solve the operator equation Tx−λx y, where T is a nonlinear operator. This paper is concerned with the numerical range in a Banach space. Nanda 15 studied the numerical range for two ...
full textA Comparative Study of Fuzzy Inner Product Spaces
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.
full textInner Product Spaces and Orthogonality
1 Dot product of R The inner product or dot product of R is a function 〈 , 〉 defined by 〈u,v〉 = a1b1 + a2b2 + · · ·+ anbn for u = [a1, a2, . . . , an] , v = [b1, b2, . . . , bn] ∈ R. The inner product 〈 , 〉 satisfies the following properties: (1) Linearity: 〈au + bv,w〉 = a〈u,w〉+ b〈v,w〉. (2) Symmetric Property: 〈u,v〉 = 〈v,u〉. (3) Positive Definite Property: For any u ∈ V , 〈u,u〉 ≥ 0; and 〈u,u〉 =...
full textNumerical Range on Weighted Hardy Spaces as Semi Inner Product Spaces
The semi-inner product, in the sense of Lumer, on weighted Hardy space which generate the norm is unique. Also we will discuss some properties of the numerical range of bounded linear operators on weighted Hardy spaces.
full textMy Resources
Journal title
volume 10 issue 1
pages 73- 83
publication date 2018-04-01
By following a journal you will be notified via email when a new issue of this journal is published.
Hosted on Doprax cloud platform doprax.com
copyright © 2015-2023