In this paper we announce the development of a functional calculus for operators defined on quaternionic Banach spaces. The definition is based on a new notion of slice regularity and the key tools are a new resolvent operator and a new eigenvalue problem. This approach allows us to deal both with bounded and unbounded operators.
A functional calculus in a non commutative setting / F. COLOMBO; G. GENTILI; I. SABADINI; D. STRUPPA. - In: ELECTRONIC RESEARCH ANNOUNCEMENTS IN MATHEMATICAL SCIENCES. - ISSN 1935-9179. - ELETTRONICO. - 14:(2007), pp. 60-68.
A functional calculus in a non commutative setting
GENTILI, GRAZIANO;
2007
Abstract
In this paper we announce the development of a functional calculus for operators defined on quaternionic Banach spaces. The definition is based on a new notion of slice regularity and the key tools are a new resolvent operator and a new eigenvalue problem. This approach allows us to deal both with bounded and unbounded operators.
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