Tensorial and Hadamard product inequalities for functions of selfadjoint operators in Hilbert spaces in terms of Kantorovich ratio

• Sever Silvestru Dragomir ^[1]
  1. [1] Mathematics, College of Engineering & Science Victoria University, PO Box 14428, Melbourne City 8001, Australia
• Localización: Extracta mathematicae, ISSN-e 0213-8743, Vol. 38, Nº 2, 2023, págs. 237-250
• Idioma: inglés
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• Resumen

  • Let H be a Hilbert space. In this paper we show among others that, if f, g are continuous on the interval I with 0 <γ ≤ f(t)/g(t)≤ Γ for t ∈ I and if A and B are selfadjoint operators with Sp (A), Sp (B) ⊂ I, then and if A and B are selfadjoint operators with Sp (A), Sp (B) ⊂ I, then The above inequalities also hold for the Hadamard product “ ◦ ” instead of tensorial product “ ⊗ ”.