Suppose that Φ(x)∈L 2(R) with compact support and V= span{Φ(x-k)|k∈Z}. In this note, we prove that if {Φ(x-k)k|k∈Z} is tight frame with bound 1 in V, then {Φ(x-k)|k∈Z} must be an orthonormal basis of V.
This paper proves the following results: Le t X= lim ←｛X σ,π σ ρ,Λ｝,｜Λ｜=λ, and every p rojection π σ: X→X σ be an open and onto mapping. (A) If X is λ-paracompact and every X σ is normal and δθ-ref...This paper proves the following results: Le t X= lim ←｛X σ,π σ ρ,Λ｝,｜Λ｜=λ, and every p rojection π σ: X→X σ be an open and onto mapping. (A) If X is λ-paracompact and every X σ is normal and δθ-refinable, then X is normal and δθ-refinable; (B) If X is hereditarily λ-pa racompact and every X σ is hereditarily normal and hereditarily δθ- refinable, then X is hereditarily normal and hereditarily δθ-refiable .展开更多
Weakly (sequentially) compactly regular inductive limits and convex weakly (sequentially) compactly regular inductive limits are investigated. (LF)-spaces satisfying Retakh's condition (M0) are convex weakly (sequ...Weakly (sequentially) compactly regular inductive limits and convex weakly (sequentially) compactly regular inductive limits are investigated. (LF)-spaces satisfying Retakh's condition (M0) are convex weakly (sequentially) compactly regular but need not be weakly (sequentially) compactly regular. For countable inductive limits of weakly sequentially complete Frechet spaces, Retakh's condition (M0) implies weakly (sequentially) compact regularity. Particularly for Kothe (LF)-sequence spaces Ep(1 ≤ p < ∞), Retakh's condition (M0) is equivalent to weakly (sequentially) compact regularity. For those spaces, the characterizations of weakly (sequentially) compact regularity are given by using the related results of Vogt.展开更多
The authors obtain function theoretic characterizations of the compactness on the standardweighted Bergman spaces of the two operators formed by multiplying a composition operatorwith the adjoint of another compositio...The authors obtain function theoretic characterizations of the compactness on the standardweighted Bergman spaces of the two operators formed by multiplying a composition operatorwith the adjoint of another composition operator.展开更多
文摘Suppose that Φ(x)∈L 2(R) with compact support and V= span{Φ(x-k)|k∈Z}. In this note, we prove that if {Φ(x-k)k|k∈Z} is tight frame with bound 1 in V, then {Φ(x-k)|k∈Z} must be an orthonormal basis of V.
文摘This paper proves the following results: Le t X= lim ←｛X σ,π σ ρ,Λ｝,｜Λ｜=λ, and every p rojection π σ: X→X σ be an open and onto mapping. (A) If X is λ-paracompact and every X σ is normal and δθ-refinable, then X is normal and δθ-refinable; (B) If X is hereditarily λ-pa racompact and every X σ is hereditarily normal and hereditarily δθ- refinable, then X is hereditarily normal and hereditarily δθ-refiable .
基金Supported by the Natural Science Foundation of the Education Committee of Jiangsu Province (Q1107107)
文摘Weakly (sequentially) compactly regular inductive limits and convex weakly (sequentially) compactly regular inductive limits are investigated. (LF)-spaces satisfying Retakh's condition (M0) are convex weakly (sequentially) compactly regular but need not be weakly (sequentially) compactly regular. For countable inductive limits of weakly sequentially complete Frechet spaces, Retakh's condition (M0) implies weakly (sequentially) compact regularity. Particularly for Kothe (LF)-sequence spaces Ep(1 ≤ p < ∞), Retakh's condition (M0) is equivalent to weakly (sequentially) compact regularity. For those spaces, the characterizations of weakly (sequentially) compact regularity are given by using the related results of Vogt.
文摘The authors obtain function theoretic characterizations of the compactness on the standardweighted Bergman spaces of the two operators formed by multiplying a composition operatorwith the adjoint of another composition operator.
