Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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APPROXIMATE IDENTITY OF CONVOLUTION BANACH ALGEBRAS

  • Han, Hyuk (Department of Liberal Arts College of Industrial Science Kongju National University)
  • Received : 2020.10.20
  • Accepted : 2020.10.29
  • Published : 2020.11.15
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Abstract

A weight ω on the positive half real line [0, ∞) is a positive continuous function such that ω(s + t) ≤ ω(s)ω(t), for all s, t ∈ [0, ∞), and ω(0) = 1. The weighted convolution Banach algebra L1(ω) is the algebra of all equivalence classes of Lebesgue measurable functions f such that ‖f‖ = ∫0∞|f(t)|ω(t)dt < ∞, under pointwise addition, scalar multiplication of functions, and the convolution product (f ⁎ g)(t) = ∫0t f(t - s)g(s)ds. We give a sufficient condition on a weight function ω(t) in order that L1(ω) has a bounded approximate identity.

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Acknowledgement

This work was supported by the research grant of the Kongju National University in 2019.

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