# Pseudo-Characters and Almost Multiplicative Functionals☆

@article{Snchez2000PseudoCharactersAA, title={Pseudo-Characters and Almost Multiplicative Functionals☆}, author={F{\'e}lix Cabello S{\'a}nchez}, journal={Journal of Mathematical Analysis and Applications}, year={2000}, volume={248}, pages={275-289} }

Ž . Let G be a multiplicative group. An e-character on G is a mapping < Ž . Ž . Ž . < f : G a T satisfying f xy y f x f y F e for all x, y g G. By a Ž . pseudo-character we mean an e-character for some usually small e ) 0. It should be noted that this term has been used with a slightly different Ž w x . meaning by a number of authors see 19 and references therein . A very w x natural question which, as far as we know, goes back to Ulam 21]24 , is whether a given pseudo-character on G must be…

## 15 Citations

### I. Ulam’s stability problem and twisted sums: two faces of a coin

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Ulam’s stability problem for additive maps and the theory of extensions of Banach spaces have remained so far unaware of each other. To support this assertion it is enough to peruse the survey…

### COMPACT FAILURE OF MULTIPLICATIVITY FOR LINEAR MAPS BETWEEN BANACH ALGEBRAS

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We introduce notions of compactness and weak compactness for multilinear maps from a product of normed spaces to a normed space, and prove some general results about these notions. We then consider…

### Stability of homomorphisms in the compact-open topology

- Mathematics
- 2010

We will prove a kind of stability result for homomorphisms from locally compact to completely regular topological universal algebras with respect to the compact-open topology on the space of all…

### Extensions of topological Abelian groups and three-space problems

- Mathematics
- 2013

A twisted sum in the category of topological abelian groups is a short exact sequence $0\to Y\to X \to Z\to 0$ where all maps are assumed to be continuous and open onto their images. The twisted sum…

### Extending Topological Abelian Groups by the Unit Circle

- Mathematics
- 2013

A twisted sum in the category of topological Abelian groups is a short exact sequence where all maps are assumed to be continuous and open onto their images. The twisted sum splits if it is…

### Stability of group homomorphisms in the compact-open topology

- Mathematics
- 2010

We introduce the notion of stability of continuous homomorphisms of topological groups with respect to the compact-open topology on the space of all continuous functions between them and prove that…

### Topological Methods in Analysis

- Mathematics
- 2013

Topological methods have played a seminal role in functional analysis since its birth in the early twentieth century. The Baire category theorem, for example, is the bedrock on which rest such basic…

### Criteria for weak and strong continuity of representations of topological groups in Banach spaces

- Mathematics
- 2002

Several necessary and sufficient conditions for weak and strong continuity of representations of topological groups in Banach spaces are obtained. In particular, it is shown that a representation of…

### Criteria for weak and strong continuity of representations of topological groups in Banach spaces

- Mathematics
- 2002

Several necessary and sufficient conditions for weak and strong continuity of representations of topological groups in Banach spaces are obtained. In particular, it is shown that a representation of…

### Locally bounded finally precontinuous finite-dimensional quasirepresentations of connected locally compact groups

- Mathematics
- 2017

We describe the structure of finite-dimensional locally bounded finally precontinuous quasirepresentations of arbitrary connected locally compact groups. Bibliography: 40 titles.

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