TY - BOOK ID - 77895858 TI - Continuous semigroups in Banach algebras PY - 1982 VL - 63. SN - 1139884069 1107366070 1107370809 1107361168 1107369908 1299403875 1107363616 0511662424 9781107361164 9780511662423 0521285984 9780521285988 PB - Cambridge Cambridge University Press DB - UniCat KW - Banach algebras. KW - Semigroups. KW - Group theory KW - Algebras, Banach KW - Banach rings KW - Metric rings KW - Normed rings KW - Banach spaces KW - Topological algebras KW - Banach algebras KW - Semigroups KW - Banach, AlgeĢbres de KW - Semi-groupes KW - Ordered algebraic structures KW - Analytical spaces UR - https://www.unicat.be/uniCat?func=search&query=sysid:77895858 AB - In these notes the abstract theory of analytic one-parameter semigroups in Banach algebras is discussed, with the Gaussian, Poisson and fractional integral semigroups in convolution Banach algebras serving as motivating examples. Such semigroups are constructed in a Banach algebra with a bounded approximate identity. Growth restrictions on the semigroup are linked to the structure of the underlying Banach algebra. The Hille-Yosida Theorem and a result of J. Esterle's on the nilpotency of semigroups are proved in detail. The lecture notes are an expanded version of lectures given by the author at the University of Edinburgh in 1980 and can be used as a text for a graduate course in functional analysis. ER -