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Sequences of independent identically distributed functions in rearrangement invariant spaces

100%

Astashkin S., Sukochev F.

Banach Center Publications

2008

tom 79

nr 1

27-37

A new set of sufficient conditions under which every sequence of independent identically distributed functions from a rearrangement invariant (r.i.) space on [0,1] spans there a Hilbertian subspace are given. We apply these results to resolve open problems of N. L. Carothers and S. L. Dilworth, and of M. Sh. Braverman, concerning such sequences in concrete r.i. spaces.

Real method of interpolation on subcouples of codimension one

100%

Astashkin S., Sunehag P.

Studia Mathematica

2008

tom 185

nr 2

151-168

We find necessary and sufficient conditions under which the norms of the interpolation spaces $(N₀,N₁)_{θ,q}$ and $(X₀,X₁)_{θ,q}$ are equivalent on N, where N is the kernel of a nonzero functional ψ ∈ (X₀ ∩ X₁)* and $N_{i}$ is the normed space N with the norm inherited from $X_{i}$ (i = 0,1). Our proof is based on reducing the problem to its partial case studied by Ivanov and Kalton, where ψ is bounded on one of the endpoint spaces. As an application we completely resolve the problem of when the range of the operator $T_{θ} = S - 2^{θ}I$ (S denotes the shift operator and I the identity) is closed in any $ℓ_{p}(μ)$, where the weight $μ = (μₙ)_{n∈ℤ}$ satisfies the inequalities $μₙ ≤ μ_{n+1} ≤ 2μₙ$ (n ∈ ℤ).

Ograniczanie wyników

1 Banach Center Publications

1 Studia Mathematica

2 Astashkin S.

1 Sukochev F.

1 Sunehag P.

2 2008

Wyniki wyszukiwania

Sequences of independent identically distributed functions in rearrangement invariant spaces

Real method of interpolation on subcouples of codimension one