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Some Norm one Functions of the Volterra Operator

  • L. Khadkhuu EMAIL logo und D. Tsedenbayar
Veröffentlicht/Copyright: 9. Februar 2016
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Mathematica Slovaca
Aus der Zeitschrift Mathematica Slovaca Band 65 Heft 6

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].

Keywords: Volterra operator; power-bounded operator; accretive operator

References

[1] HALMOS, P. R.: A Hilbert Space Problem Book, Van Nostrand, Princeton, NJ, 1967.Suche 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/sm199-2-3Suche 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.Suche in Google Scholar

[4] TSEDENBAYAR, D.: On the power boundedness of certain Volterra operator pencils, Studia Math. 156 (2003), 59-66.10.4064/sm156-1-4Suche 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

Artikel in diesem Heft

  1. Radius, Diameter and the Degree Sequence of a Graph
  2. On Primary Ideals in Posets
  3. Characterization of the Set of Regular Elements in Ordered Semigroups
  4. Tame Automorphisms with Multidegrees in the Form of Arithmetic Progressions
  5. A Result Concerning Additive Mappings in Semiprime Rings
  6. Characterizing Jordan Derivations of Matrix Rings Through Zero Products
  7. Existence Results for Impulsive Nonlinear Fractional Differential Equations With Nonlocal Boundary Conditions
  8. The Radon-Nikodym Property and the Limit Average Range
  9. A Hake-Type Theorem for Integrals with Respect to Abstract Derivation Bases in the Riesz Space Setting
  10. On Booth Lemniscate and Hadamard Product of Analytic Functions
  11. Recursion Formulas for Srivastava Hypergeometric Functions
  12. Regularly Varying Solutions of Half-Linear Diffferential Equations with Retarded and Advanced Arguments
  13. Singular Degenerate Differential Operators and Applications
  14. The Interior Euler-Lagrange Operator in Field Theory
  15. On Selections of Set-Valued Maps Satisfying Some Inclusions in a Single Variable
  16. The Family F of Permutations of ℕ
  17. Summation Process of Positive Linear Operators in Two-Dimensional Weighted Spaces
  18. On Iλ-Statistical Convergence in Locally Solid Riesz Spaces
  19. Some Norm one Functions of the Volterra Operator
  20. Some Results on Absolute Retractivity of the Fixed Points Set of KS-Multifunctions
  21. Convexity in the Khalimsky Plane
  22. Natural Boundary Conditions in Geometric Calculus of Variations
  23. Exponential Inequalities for Bounded Random Variables
  24. Precise Rates in the Law of Iterated Logarithm for the Moment Convergence of φ-Mixing Sequences
  25. Second Order Riemannian Mechanics
  26. Further Remarks on an Order for Quantum Observables
https://doi.org/10.1515/ms-2015-0102
Schlagwörter für diesen Artikel
Volterra operator; power-bounded operator; accretive operator

Artikel in diesem Heft

  1. Radius, Diameter and the Degree Sequence of a Graph
  2. On Primary Ideals in Posets
  3. Characterization of the Set of Regular Elements in Ordered Semigroups
  4. Tame Automorphisms with Multidegrees in the Form of Arithmetic Progressions
  5. A Result Concerning Additive Mappings in Semiprime Rings
  6. Characterizing Jordan Derivations of Matrix Rings Through Zero Products
  7. Existence Results for Impulsive Nonlinear Fractional Differential Equations With Nonlocal Boundary Conditions
  8. The Radon-Nikodym Property and the Limit Average Range
  9. A Hake-Type Theorem for Integrals with Respect to Abstract Derivation Bases in the Riesz Space Setting
  10. On Booth Lemniscate and Hadamard Product of Analytic Functions
  11. Recursion Formulas for Srivastava Hypergeometric Functions
  12. Regularly Varying Solutions of Half-Linear Diffferential Equations with Retarded and Advanced Arguments
  13. Singular Degenerate Differential Operators and Applications
  14. The Interior Euler-Lagrange Operator in Field Theory
  15. On Selections of Set-Valued Maps Satisfying Some Inclusions in a Single Variable
  16. The Family F of Permutations of ℕ
  17. Summation Process of Positive Linear Operators in Two-Dimensional Weighted Spaces
  18. On Iλ-Statistical Convergence in Locally Solid Riesz Spaces
  19. Some Norm one Functions of the Volterra Operator
  20. Some Results on Absolute Retractivity of the Fixed Points Set of KS-Multifunctions
  21. Convexity in the Khalimsky Plane
  22. Natural Boundary Conditions in Geometric Calculus of Variations
  23. Exponential Inequalities for Bounded Random Variables
  24. Precise Rates in the Law of Iterated Logarithm for the Moment Convergence of φ-Mixing Sequences
  25. Second Order Riemannian Mechanics
  26. Further Remarks on an Order for Quantum Observables
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