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Replacing the triangle inequality, in the definition of a norm, by ‖x + y‖ q ≤ 2 (‖x‖ q + ‖y‖ q ), we introduce the notion of a q-norm. We establish that every q-norm is a norm in the usual sense,… (More)

Abstract. Utilizing the Birkhoff–James orthogonality, we present some characterizations of the norm-parallelism for elements of B(H ) defined on a finite dimensional Hilbert space, elements of a… (More)

- A. H. Ansari, Mohammad Sal Moslehian
- Int. J. Math. Mathematical Sciences
- 2005

Refining some results of Dragomir, several new reverses of the generalized triangle inequality in inner product spaces are given. Among several results, we establish some reverses for the Schwarz… (More)

We study the Cauchy--Schwarz and some related inequalities in a semi-inner product module over a $C^*$-algebra $\A$. The key idea is to consider a semi-inner product $\A$-module as a semi-inner… (More)

In this paper, we prove that if $$\Phi : \mathscr {A} \rightarrow \mathscr {B}$$Φ:A→B is a bounded linear map between $$C^*$$C∗-algebras, then $$\begin{aligned} \left\| \sum _{k=1}^n \left\{ |\Phi… (More)

Let $\mathfrak{M}$ be a semifinite von Neumann algebra on a Hilbert space equipped with a faithful normal semifinite trace $\tau$. A closed densely defined operator $x$ affiliated with $\mathfrak{M}$… (More)

Let n denote the algebra of all n×n complex matrices A with entries inC, together with the usual matrix operations. By an algebra norm (or a matrix norm) we mean a norm ‖·‖ on n such that ‖AB‖ ≤… (More)