In this paper, the hereditarily almost expandability of inverse limits is investigated, with two results obtained. Let X be the inverse limit space of an inverse system （Xα, π^αβ, ∧}. （1） Suppose X is heredita...In this paper, the hereditarily almost expandability of inverse limits is investigated, with two results obtained. Let X be the inverse limit space of an inverse system （Xα, π^αβ, ∧}. （1） Suppose X is hereditarily κ-metacompact, if each Xα is hereditarily pointwise collectionwise normal （almost θ-expandable, almost discrete θ-expandable）, then so is X; （2） Suppose X is hereditarily κ-σ-metacompact, if each Xα is hereditarily almost σ-expandable （almost discrete σ-expandable = σ-pointwise collectionwise normal）, then so is X.展开更多
In this paper we first discuss the relations between some G-M-type spaces, and the previous eight kinds of G-M-type Banach spaces are merged into four different kinds. Then we build a Generalized Operator Extension Th...In this paper we first discuss the relations between some G-M-type spaces, and the previous eight kinds of G-M-type Banach spaces are merged into four different kinds. Then we build a Generalized Operator Extension Theorem, and introduce the concept of complete minimal sequences. Some sufficient and necessary conditions under which a Banach space is a hereditarily indecomposable space are given. Finally, we give some characterizations of hereditarily indecomposable Banach Spaces.展开更多
Let {Xi,πki,ω} be an inverse sequence and X -- lim{Xi,πki,ω）. If each Xi is hereditarily （resp. metaLindelSf, σ-metaLindelSf, σ-orthocompact, weakly suborthocompact, δθ-refinable, weakly θ-refinable, weakly...Let {Xi,πki,ω} be an inverse sequence and X -- lim{Xi,πki,ω）. If each Xi is hereditarily （resp. metaLindelSf, σ-metaLindelSf, σ-orthocompact, weakly suborthocompact, δθ-refinable, weakly θ-refinable, weakly δθ-refinable）, then so is X.展开更多
This paper shows that every non-separable hereditarily indecomposable Banach space admits an equivalent strictly convex norm, but its bi-dual can never have such a one; consequently, every non-separable hereditarily i...This paper shows that every non-separable hereditarily indecomposable Banach space admits an equivalent strictly convex norm, but its bi-dual can never have such a one; consequently, every non-separable hereditarily indecomposable Banach space has no equivalent locally uniformly convex norm.展开更多
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
In this paper, we characterize conditions under which a tuple of bounded linear operators is topologically mixing. Also, we give conditions for a tuple to be hereditarily hypercyclic with respect to a tuple of syndeti...In this paper, we characterize conditions under which a tuple of bounded linear operators is topologically mixing. Also, we give conditions for a tuple to be hereditarily hypercyclic with respect to a tuple of syndetic sequences.展开更多
t In this note, we present that： （1） Let X=o{X,, ： a C A} be ｜A｜-paracompact （resp., hereditarily ｜A｜-paracompact）. If every finite subproduct of {Xa： a C A} has property bl （resp., hereditarily property b...t In this note, we present that： （1） Let X=o{X,, ： a C A} be ｜A｜-paracompact （resp., hereditarily ｜A｜-paracompact）. If every finite subproduct of {Xa： a C A} has property bl （resp., hereditarily property bl）, then so is X. （2） Let X be a P-space and Y a metric space. Then, X x Y has property bl iff X has property bl. （3） Let X be a strongly zero-dimensionM and compact space. Then, X x Y has property bl iff Y has property bl.展开更多
RECENTLY Gowers and Maurey constructed the first example of Banach space containing no unconditional basic sequence. We denote this space by X_G, in this note. Using the results in ref. [1], some further studies and r...RECENTLY Gowers and Maurey constructed the first example of Banach space containing no unconditional basic sequence. We denote this space by X_G, in this note. Using the results in ref. [1], some further studies and reconstructions of this space result in some satisfactory answers of a series of open questions in the Banach spaces theory. There is a general description about this remarkable development. Just as indicated in ref. [1], the most important characteristic of the Banach space X_G展开更多
Suppose that X, Y are two real Banach Spaces. We know that for a standard ε-isometry f : X → Y, the weak stability formula holds and by applying the formula we can induce a closed subspace N of *. In this paper, by ...Suppose that X, Y are two real Banach Spaces. We know that for a standard ε-isometry f : X → Y, the weak stability formula holds and by applying the formula we can induce a closed subspace N of *. In this paper, by using again the weak stability formula, we further show a sufficient and necessary condition for a standard ε-isometry to be stable in assuming that N is w*-closed in Y*.Making use of this result, we improve several known results including Figiel’s theorem in reflexive spaces.We also prove that if, in addition, the space Y is quasi-reflexive and hereditarily indecomposable, then L(f)≡span[f(X)] contains a complemented linear isometric copy of X;Moreover, if X =Y, then for every e-isometry f: X → X, there exists a surjective linear isometry S:X → X such that f-S is uniformly bounded by 2ε on X.展开更多
Let l=[0,1] and ω<sub>0</sub> be the first limit ordinal number. Assume that f:l→l is continuous, piece-wise monotone and the set of periods of f is {2<sup>i</sup>: i∈{0}∪N}. It is known th...Let l=[0,1] and ω<sub>0</sub> be the first limit ordinal number. Assume that f:l→l is continuous, piece-wise monotone and the set of periods of f is {2<sup>i</sup>: i∈{0}∪N}. It is known that the order of （l, f） is ω<sub>0</sub> or ω<sub>0</sub> + 1. It is shown that the order of the inverse limit space （l, f） is ω<sub>0</sub> （resp. ω<sub>0</sub> + 1） if and only if f is not （resp. is） chaotic in the sense of Li-Yorke.展开更多
基金Supported by the Scientific Fund of the Educational Committee of Xinjiang of China (XJEDU2004158)
文摘In this paper, the hereditarily almost expandability of inverse limits is investigated, with two results obtained. Let X be the inverse limit space of an inverse system （Xα, π^αβ, ∧}. （1） Suppose X is hereditarily κ-metacompact, if each Xα is hereditarily pointwise collectionwise normal （almost θ-expandable, almost discrete θ-expandable）, then so is X; （2） Suppose X is hereditarily κ-σ-metacompact, if each Xα is hereditarily almost σ-expandable （almost discrete σ-expandable = σ-pointwise collectionwise normal）, then so is X.
基金The NNSF (10471025) of China the Foundation (JA04170) of the Education Department of Fujian Province, China.
文摘In this paper we first discuss the relations between some G-M-type spaces, and the previous eight kinds of G-M-type Banach spaces are merged into four different kinds. Then we build a Generalized Operator Extension Theorem, and introduce the concept of complete minimal sequences. Some sufficient and necessary conditions under which a Banach space is a hereditarily indecomposable space are given. Finally, we give some characterizations of hereditarily indecomposable Banach Spaces.
文摘Let {Xi,πki,ω} be an inverse sequence and X -- lim{Xi,πki,ω）. If each Xi is hereditarily （resp. metaLindelSf, σ-metaLindelSf, σ-orthocompact, weakly suborthocompact, δθ-refinable, weakly θ-refinable, weakly δθ-refinable）, then so is X.
基金Research supported by NSFC(Grant No.10471114 and No.10471025)
文摘This paper shows that every non-separable hereditarily indecomposable Banach space admits an equivalent strictly convex norm, but its bi-dual can never have such a one; consequently, every non-separable hereditarily indecomposable Banach space has no equivalent locally uniformly convex norm.
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 .
文摘In this paper, we characterize conditions under which a tuple of bounded linear operators is topologically mixing. Also, we give conditions for a tuple to be hereditarily hypercyclic with respect to a tuple of syndetic sequences.
基金Supported by the National Natural Science Foundation of China (Grant Nos. 1067113411026081)
文摘t In this note, we present that： （1） Let X=o{X,, ： a C A} be ｜A｜-paracompact （resp., hereditarily ｜A｜-paracompact）. If every finite subproduct of {Xa： a C A} has property bl （resp., hereditarily property bl）, then so is X. （2） Let X be a P-space and Y a metric space. Then, X x Y has property bl iff X has property bl. （3） Let X be a strongly zero-dimensionM and compact space. Then, X x Y has property bl iff Y has property bl.
文摘RECENTLY Gowers and Maurey constructed the first example of Banach space containing no unconditional basic sequence. We denote this space by X_G, in this note. Using the results in ref. [1], some further studies and reconstructions of this space result in some satisfactory answers of a series of open questions in the Banach spaces theory. There is a general description about this remarkable development. Just as indicated in ref. [1], the most important characteristic of the Banach space X_G
基金supported in part by the Natural Science Foundation of China(Grant Nos.11731010,11471270&11471271)
文摘Suppose that X, Y are two real Banach Spaces. We know that for a standard ε-isometry f : X → Y, the weak stability formula holds and by applying the formula we can induce a closed subspace N of *. In this paper, by using again the weak stability formula, we further show a sufficient and necessary condition for a standard ε-isometry to be stable in assuming that N is w*-closed in Y*.Making use of this result, we improve several known results including Figiel’s theorem in reflexive spaces.We also prove that if, in addition, the space Y is quasi-reflexive and hereditarily indecomposable, then L(f)≡span[f(X)] contains a complemented linear isometric copy of X;Moreover, if X =Y, then for every e-isometry f: X → X, there exists a surjective linear isometry S:X → X such that f-S is uniformly bounded by 2ε on X.
文摘Let l=[0,1] and ω<sub>0</sub> be the first limit ordinal number. Assume that f:l→l is continuous, piece-wise monotone and the set of periods of f is {2<sup>i</sup>: i∈{0}∪N}. It is known that the order of （l, f） is ω<sub>0</sub> or ω<sub>0</sub> + 1. It is shown that the order of the inverse limit space （l, f） is ω<sub>0</sub> （resp. ω<sub>0</sub> + 1） if and only if f is not （resp. is） chaotic in the sense of Li-Yorke.
