## Taiwanese Journal of Mathematics

### A NOTE ON THE CONTINUITY OF OPERATORS INTERTWINING WITH CONVOLUTION OPERATORS

#### Abstract

Let $G$ be a MAP group, let $\mu$ be a bounded complex-valued Borel measure on $G$, and let $T_{\mu}$ be the corresponding convolution operator on $L^{1}(G)$. Let $X$ be a Banach space and let $S$ be a continuous linear operator on $X$. We show that every linear operator $\Phi:X \rightarrow L^{1}(G)$ such that $\Phi S = T_{\mu} \Phi$ is continuous if, and only if, the pair $(S,T_{\mu})$ has no critical eigenvalue.

#### Article information

Source
Taiwanese J. Math., Volume 12, Number 2 (2008), 337-340.

Dates
First available in Project Euclid: 20 July 2017

https://projecteuclid.org/euclid.twjm/1500574158

Digital Object Identifier
doi:10.11650/twjm/1500574158

Mathematical Reviews number (MathSciNet)
MR2402119

Zentralblatt MATH identifier
1157.46025

#### Citation

Alaminos, J.; Extremera, J.; Villena, A. R. A NOTE ON THE CONTINUITY OF OPERATORS INTERTWINING WITH CONVOLUTION OPERATORS. Taiwanese J. Math. 12 (2008), no. 2, 337--340. doi:10.11650/twjm/1500574158. https://projecteuclid.org/euclid.twjm/1500574158

#### References

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