Bentuo Zheng

REMARKS ON LIPSCHITZ p-SUMMING OPERATORS

In this paper, a nonlinear version of the Extrapolation Theorem is proved and, as a corollary, a nonlinear version of Grothendiecks Theorem is presented. Finally, we prove that if T: X → H is Lipschitz with X being a pointed metric space and T(0) = 0 such that T # | H * is q-summing (1 ≤ q < oo), then T is Lipschitz 1-summing.

A Characterization of Schauder Frames Which Are Near-Schauder Bases

A basic problem of interest in connection with the study of Schauder frames in Banach spaces is that of characterizing those Schauder frames which can essentially be regarded as Schauder bases. In this paper, we give a solution to this problem using the notion of the minimal-associated sequence spaces and the minimal-associated reconstruction operators for Schauder frames. We prove that a Schauder frame is a near-Schauder basis if and only if the kernel of the minimal-associated reconstruction operator contains no copy of c0. In particular, a Schauder frame of a Banach space with no copy of c0 is a near-Schauder basis if and only if the minimal-associated sequence space contains no copy of c0. In these cases, the minimal-associated reconstruction operator has a finite dimensional kernel and the dimension of the kernel is exactly the excess of the near-Schauder basis. Using these results, we make related applications on Besselian frames and near-Riesz bases.

Norm closed ideals in the algebra of bounded linear operators on Orlicz sequence spaces

For each 1 < p < ∞, we consider a class of p-regular Orlicz sequence spaces M that are “close” to p and study the structure of the norm closed ideals in the algebra of bounded linear operators on such spaces. We show that the unique maximal ideal in L( M ) is the set of all M strictly singular operators and the immediate successor of the ideal of compact operators in L( M ) is the closed ideal generated by the formal identity from M into p.

Systems formed by translates of one element in _{}(ℝ)

Let

Stability of ball proximinality

1\le p 4

Circular operators on minimal norm ideals of ℬ(ℋ)

, there exists

Geometric properties on non-complete spaces

f\in L_p(\real)

The weak bounded approximation property of pairs

and

Strict isometries of arbitrary orders

\Lambda \subseteq \zed

Commutators on

so that