2025/03/03 by Augustine, Athul, Bhunia, Pintu, Shankar, P.
#26E60 #46L05 #47A12 #47A30 #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)
paper · doi:10.48550/arxiv.2503.01331
We introduce a new family of non-negative real-valued functions on a C^*-algebra A, i.e., for 0≤ μ≤ 1, ‖a‖σμ= sup\lbrace √(|f(a)|2 σμ f(a^*a)): f∈ A', f(1)=‖f‖=1 \rbrace, where a∈ A and σμ is an interpolation path of the symmetric mean σ. These functions are semi-norms as they satisfy the norm axioms, except for the triangle inequality. Special cases satisfying triangle inequality, and a complete equality characterization is also discussed. Various bounds and relationships will be established for this new family, with a connection to the existing literature in the algebra of all bounded linear operators on a Hilbert space.