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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Semigroups over real alternative *-algebras: Generation theorems and spherical sectorial operators
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by Riccardo Ghiloni and Vincenzo Recupero PDF
Trans. Amer. Math. Soc. 368 (2016), 2645-2678 Request permission


The aim of this paper is twofold. On one hand, generalizing some recent results obtained in the quaternionic setting, but using simpler techniques, we prove the generation theorems for semigroups in Banach spaces whose set of scalars belongs to the class of real alternative *-algebras, which includes, besides real and complex numbers, quaternions, octonions and Clifford algebras. On the other hand, in this new general framework, we introduce the notion of spherical sectorial operator and we prove that a spherical sectorial operator generates a semigroup that can be represented by a Cauchy integral formula. It follows that such a semigroup is analytic in time.
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Additional Information
  • Riccardo Ghiloni
  • Affiliation: Dipartimento di Matematica, Università di Trento, Via Sommarive 14, 38123 Povo-Trento (TN), Italy
  • MR Author ID: 699436
  • Email:
  • Vincenzo Recupero
  • Affiliation: Dipartimento di Scienze Matematiche, Politecnico di Torino, Corso Duca degli, Abruzzi 24, 10129 Torino, Italy
  • MR Author ID: 692450
  • Email:
  • Received by editor(s): December 3, 2013
  • Received by editor(s) in revised form: January 26, 2014
  • Published electronically: April 14, 2015
  • © Copyright 2015 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 368 (2016), 2645-2678
  • MSC (2010): Primary 30G35, 47D03, 47A60, 47A10
  • DOI:
  • MathSciNet review: 3449252