A note on C0-groups and C-groups on non-archimedean Banach spaces

Abstract

In this paper, we introduce new classes of linear operators so called [Formula: see text]-groups, [Formula: see text]-groups and cosine families of bounded linear operators on non-archimedean Banach spaces over non-archimedean complete valued field [Formula: see text]. We show some results about it.

Pseudo-spectrum of non-Archimedean matrix pencils

“…We denote the completion of algebraic closure of Q p under the p-adic valuation | • | p by C p [11]. For more details on non-Archimedean pseudo-spectrum of operator pencils or matrix pencils, we refer to [4], [5] and [6]. In this paper, we study the problem of finding the eigenvalues of the generalized eigenvalue problem Ax = λBx for λ ∈ K and x ∈ K n , M n (K) denotes the algebra of all n × n (n.a) matrices and I is the n × n identity matrix.…”

Some integrals for groups of bounded linear operators on finite-dimensional non-Archimedean Banach spaces

“…For more details, we refer to [2], [4] and [9]. But there is a different results in non-Archimedean analysis, by [2], Theorem 1, we have: Recently, Diagana [3] introduced the notion of C 0 -groups of bounded linear operators on a free non-Archimedean Banach space, for more details we refer to [3] and [5].…”

“…In [5], A. El Amrani, A. Blali, J. Ettayb and M. Babahmed introduced the notions of C-groups and cosine families of bounded linear operators on non-Archimedean Banach space. Let r > 0, Ω r = {t ∈ K : |t| < r} [5]. We have the following definition.…”

$C$-groups and mixed $C$-groups of bounded linear operators on non-archimedean Banach spaces

“…In non-archimedean operator theory, T. Diagana [2] introduced the concept of C 0 -groups of bounded linear operators on free non-archimedean Banach space. Also, in [5], A. El Amrani, A. Blali, J. Ettayb and M. Babahmed introduced and studied the notions of C-groups and cosine family of bounded linear operators on non-archimedean Banach space. As an application of C-groups of linear operators is the p-adic abstract Cauchy problem for differential equations on a non-archimedean 186 A. EL AMRANI, A. BLALI, AND J. ETTAYB Banach space X given by ACP(A; x)…”

“…In the non-archimedean context, a family (T (t)) t∈Ωr ⊆ B(X) is called a group of bounded linear operators if T (0) = I and for all t, s ∈ Ω r , T (t + s) = T (t)T (s), where I is the unit operator of X. For more details, we refer to [2,5].…”