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Entropy Numbers of Certain Summation Operators
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J. Creutzig
Published/Copyright:
February 25, 2010
Abstract
Given nonnegative real sequences 
and 
we study the generated summation operator
regarded as a mapping from ℓp(ℤ) to ℓq(ℤ). We give necessary and sufficient conditions for the boundedness of S𝑎, 𝑏 and prove optimal estimates for its entropy numbers relative to the summation properties of 𝑎 and 𝑏. Our results are applied to the investigation of the behaviour of
as ε → 0, where 
is some nondecreasing sequence in [0, ∞) and (W(t))t ≥ 0 denotes the Wiener process.
Received: 2000-07-08
Published Online: 2010-02-25
Published in Print: 2001-June
© Heldermann Verlag
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Articles in the same Issue
- Topological Spaces with the Strong Skorokhod Property
- Convergence to Zero and Boundedness of Operator-Normed Sums of Random Vectors with Application to Autoregression Processes
- On a Characterisation of Inner Product Spaces
- On the Tail Estimation of the Norm of Rademacher Sums
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- Proper Moving Average Representations and Outer Functions in Two Variables
- Sequential Compactness for the Weak Topology of Vector Measures in Certain Nuclear Spaces
- Towards an Innovation Theory of Spatial Brownian Motion under Boundary Conditions
- Entropy Numbers of Diagonal Operators of Logarithmic Type
- On Normal Approximation of Large Products of Functions: A Refinement of Blackwell's Result
- Asymptotic Behavior of Singular and Entropy Numbers for Some Riemann–Liouville Type Operators
- Probability Measures with Big Kernels
- Hölder Versions of Banach Space Valued Random Fields
- Representations of Conditional Means
- On Convergence of Series of Random Elements via Maximal Moment Relations with Applications to Martingale Convergence and to Convergence of Series with p-Orthogonal Summands
- On Stochastic Differential Equations in a Configuration Space
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