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Some Norm one Functions of the Volterra Operator
-
L. Khadkhuu
and
D. Tsedenbayar
Published/Copyright:
February 9, 2016
Abstract
Let B be an accretive operator on a complex Hilbert space and let V be the classical Volterra operator on L2(0, 1). We study a contraction property for (I −mB)(I +B)−1, m ∈ ℝ. In particular, we show that ‖(I −mV)(I+V)−1‖ = 1 only for m ∈ [−1, 1].
References
[1] HALMOS, P. R.: A Hilbert Space Problem Book, Van Nostrand, Princeton, NJ, 1967.Search in Google Scholar
[2] LYUBICH, YU.-TSEDENBAYAR, D.: The norms and singular numbers of polynomials of the classical Volterra operator, Studia Math. 199 (2010), 171-184.10.4064/sm199-2-3Search in Google Scholar
[3] NIKOLSKI, N. K.: Operators, Functions and Systems: An Easy Reading, Vol 2: Model Opeartors and Systems, Amer. Math. Soc., Providence, RI, 2002.Search in Google Scholar
[4] TSEDENBAYAR, D.: On the power boundedness of certain Volterra operator pencils, Studia Math. 156 (2003), 59-66.10.4064/sm156-1-4Search in Google Scholar
Received: 2012-10-20
Accepted: 2013-1-15
Published Online: 2016-2-9
Published in Print: 2015-12-1
Mathematical Institute Slovak Academy of Sciences
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- On Primary Ideals in Posets
- Characterization of the Set of Regular Elements in Ordered Semigroups
- Tame Automorphisms with Multidegrees in the Form of Arithmetic Progressions
- A Result Concerning Additive Mappings in Semiprime Rings
- Characterizing Jordan Derivations of Matrix Rings Through Zero Products
- Existence Results for Impulsive Nonlinear Fractional Differential Equations With Nonlocal Boundary Conditions
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- A Hake-Type Theorem for Integrals with Respect to Abstract Derivation Bases in the Riesz Space Setting
- On Booth Lemniscate and Hadamard Product of Analytic Functions
- Recursion Formulas for Srivastava Hypergeometric Functions
- Regularly Varying Solutions of Half-Linear Diffferential Equations with Retarded and Advanced Arguments
- Singular Degenerate Differential Operators and Applications
- The Interior Euler-Lagrange Operator in Field Theory
- On Selections of Set-Valued Maps Satisfying Some Inclusions in a Single Variable
- The Family F of Permutations of ℕ
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- Exponential Inequalities for Bounded Random Variables
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