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.
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 operat
Definition 1. An inner product on a complex vector space V is a map 〈., .〉 : V × V → C such that (i) 〈., .〉 is linear in the first slot: 〈c1v1 + c2v2, w〉 = c1〈v1, w〉+ c2〈v2, w〉, c1, c2 ∈ C, v1, v2, w ∈ V, (ii) 〈., .〉 is Hermitian symmetric: 〈v, w〉 = 〈w, v〉, with the bar denoting
The concepts of 2−inner products and 2−inner product spaces have been intensively studied by many authors in the last three decades. A systematic presentation of the recent results related to the theory of 2−inner product spaces as well as an extensive list of the related referen
In 1964, Gähler 1 introduced the concept of 2-norm and 2-inner product spaces as generalization of norm and inner product spaces. A systematic presentation of the results related to the theory of 2-inner product spaces can be found in the book in 2, 3 and in list of references in
We present a generalization of Wigner’s unitary-antiunitary theorem for pairs of ray transformations. As a particular case, we get a new Wigner-type theorem for non-Hermitian indefinite inner product spaces. The classical Wigner unitary-antiunitary theorem plays a fundamental rol
has been introduced by several authors like Ahmed and Hamouly [1], Kohli and Kumar [5], Biswas [4], etc. Also the notion of fuzzy norm on a linear space was introduced by Katsaras [9]. Later on many other mathematicians like Felbin [3], Cheng and Mordeso [10], Bag and Samanta [6]