On some norm equalities in pre-Hilbert \(C^{\ast}\)-modules

DOI10.1016/j.laa.2005.09.006zbMath1100.47006OpenAlexW2083378146MaRDI QIDQ819755

Rajna Rajić, Ljiljana Arambašić

Publication date: 29 March 2006

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2005.09.006

zbMATH Keywords

numerical rangetriangle inequalityHilbert \(C^{*}\)-module\(C^{*}\)-algebraPythagoras' equality

Mathematics Subject Classification ID

Norms (inequalities, more than one norm, etc.) of linear operators (47A30) (C^*)-modules (46L08) Numerical range, numerical radius (47A12)

Related Items (10)

Birkhoff–James Orthogonality: Characterizations, Preservers, and Orthogonality Graphs ⋮ \(\mathcal{A}\)-valued norm parallelism in Hilbert \(\mathcal{A}\)-modules ⋮ The Dunkl-Williams equality in pre-Hilbert \(C^{*}\)-modules ⋮ On Birkhoff-James and Roberts orthogonality ⋮ The Birkhoff-James orthogonality in Hilbert \(C^{\ast }\)-modules ⋮ Norm equalities in pre-Hilbert \(C^{*}\)-modules ⋮ Birkhoff-James orthogonality and applications: a survey ⋮ On the \(C^*\)-valued triangle equality and inequality in Hilbert \(C^*\)-modules ⋮ Operator equalities and Characterizations of Orthogonality in Pre-Hilbert C*-Modules ⋮ Characterization of equality in a generalized Dunkl-Williams inequality

Cites Work

• Matricial ranges of quadratic operators
• Growth conitions and the numerical range in a Banach algebra
• Inner derivations and norm equality
• The unilateral shift and a norm equality for bounded linear operators
• The numerical range of a nilpotent operator on a Hilbert space
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