# On Property (M) and Its Generalizations

@article{Xu2001OnP, title={On Property (M) and Its Generalizations}, author={Hong-Kun Xu and Giuseppe Marino and Paolamaria Pietramala}, journal={Journal of Mathematical Analysis and Applications}, year={2001}, volume={261}, pages={271-281} }

Abstract Properties strict (M) and uniform (M) are introduced. It is shown that if X has property (M) and is uniformly convex in every direction, then X has both strict (M) and uniform (M). It is also shown that if X* is separable, then strict (M) implies uniform (M) and property (M) implies weak uniform normal structure. Relations with other geometrical properties of Banach spaces are also discussed.

## 4 Citations

### Smoothness, asymptotic smoothness and the Blum-Hanson property

- Mathematics
- 2016

We isolate various sufficient conditions for a Banach space X to have the so-called Blum-Hanson property. In particular, we show that X has the Blum-Hanson property if either the modulus of…

### Some Topological and Geometric Properties of Some New Spaces of -Convergent and Bounded Series

- Mathematics
- 2015

The main purpose of this study is to introduce the spaces , , and which are -spaces of nonabsolute type. We prove that these spaces are linearly isomorphic to the spaces , , and , respectively, and…

### A note on properties that imply the fixed point property

- Mathematics
- 2006

We give relationships between some Banach-space geometric
properties that guarantee the weak fixed point property. The
results extend some known results
of Dalby and Xu.

## References

SHOWING 1-10 OF 13 REFERENCES

### Property (M) and the weak fixed point property

- Mathematics
- 1997

It is shown that in Banach spaces with the property (M) of Kalton, nonexpansive self mappings of nonempty weakly compact convex sets necessarily have fixed points. The stability of this conclusion…

### Topological properties of Banach spaces

- Mathematics
- 1984

Let I b e a Banach space, Bx its closed unit ball. We study several topological properties of Bx with its weak topology. In particular, we consider spaces X such that (Bx, weak) is a Polish…

### $M$-ideals of compact operators

- Mathematics
- 1993

If X is a Banach space and E is a subspace of X then E is called an M-ideal in X if X* can be decomposed an/1-sum X* E +/1V for some closed subspace V of X*. This notion was introduced by Alfsen and…

### Espaces de Banach stables

- Mathematics
- 1981

We define the notion of “stable Banach space” by a simple condition on the norm. We prove that ifE is a stable Banach space, then every subspace ofLp(E) (1≦p<∞) is stable. Our main result asserts…

### Asymptotically Isometric Copies ofc0and Renormings of Banach Spaces

- Mathematics
- 1998

Abstract If a Banach space X contains an asymptotically isometric copy of c 0 , then X fails to have weak normal structure. Consequently, if X is an infinite-dimensional subspace of ( c 0 , ‖ · ‖ ∞…

### NORMAL STRUCTURE COEFFICIENTS FOR BANACH SPACES

- Mathematics
- 1980

1* Definitions. The concepts introduced in this paper are phrased in terms of reflexive Banach spaces. This is not a serious restriction, but rather one of technical convenience. All of the concepts…

### Stability of weak normal structure in James quasi reflexive space

- MathematicsBulletin of the Australian Mathematical Society
- 1992

We introduce a coefficient on general Banach spaces which allows us to derive the weak normal structure for those Banach spaces whose Banach-Mazur distance to James quasi reflexive space is less than…