Glasnik Matematicki, Vol. 43, No.2 (2008), 423-437.

REPRESENTATION THEOREMS FOR OPERATORS OF TYPE lp,qv,ω,ψ AND Sω,ψ

M. Gupta and L. R. Acharya

Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, U.P.- 208016, India
e-mail: manjul@iitk.ac.in
e-mail: lipi@iitk.ac.in

Abstract.   Let 0 < p, q ≤ ∞, and ψ : [0, ∞) → [0, ∞) be a continuous, strictly increasing, subadditive function which satisfies ψ(0) = 0. For sequences v = {vn}, ω = {ωn} of positive numbers we define sequence classes lp,qv,ω,ψ and Sω,ψ and give representation theorems for an operator of type lp,qv,ω,ψ and Sω,ψ.

2000 Mathematics Subject Classification.   47B06.

Key words and phrases.   Approximation numbers, sequence spaces.

Full text (PDF) (free access)

DOI: 10.3336/gm.43.2.13

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