APPROXIMATE IDENTITY OF CONVOLUTION BANACH ALGEBRAS

• Published in: 충청수학회지, 33(4) pp. 497 - 504
• Main Author: 한혁
• Format: Journal Article
• Language: English
• Published: 충청수학회 01.11.2020
• Subjects: 수학
• ISSN: 1226-3524; 2383-6245
• DOI: 10.14403/jcms.2020.33.4.497

A weight $\omega$ on the positive half real line $[0, \infty)$ is a positive continuous function such that $\omega(s+t) \le \omega(s)\omega(t)$, for all $s, t\in [0,\infty)$, and $\omega(0)=1$. The weighted convolution Banach algebra $L^1(\omega)$ is the algebra of all equivalence classes of Lebesgue measurable functions $f$ such that $\|f \| = \int_0^\infty|f(t)| \, \omega(t) \text{dt} < \infty$, under pointwise addition, scalar multiplication of functions, and the convolution product $(f*g)(t)=\int_0^t f(t-s) g(s) \text{ds}$. We give a sufficient condition on a weight function $\omega(t)$ in order that $L^1(\omega)$ has a bounded approximate identity. KCI Citation Count: 0