Unbounded Normal Operators in Octonion Hilbert Spaces and Their
Unbounded normal operators in octonion Hilbert spaces and their spectra Ludkovsky S.V. 15 February 2012 Abstract Affiliated and normal operators in octonion Hilbert spaces are studied. Theorems about their properties and of related algebras are demonstrated. Spectra of unbounded normal operators are investi- gated. 1 1 Introduction Unbounded normal operators over the complex field have found many-sided applications in functional analysis, differential and partial differential equa- tions and their applications in the sciences [4, 11, 12, 14, 31]. On the other hand, hypercomplex analysis is fast developing, particularly in relation with problems of theoretical and mathematical physics and of partial differential equations [2, 7, 9]. The octonion algebra is the largest division real algebra arXiv:1204.1554v1 [math.FA] 6 Apr 2012 in which the complex field has non-central embeddings [3, 1, 13]. It is inten- sively used especially in recent years not only in mathematics, but also in applications [5, 10, 8, 15, 16]. In previous works analysis over quaternion and octonions was developed and spectral theory of bounded normal operators and unbounded self-adjoint 1key words and phrases: non-commutative functional analysis, hypercomplex numbers, quaternion skew field, octonion algebra, operator, operator algebra, spectra, spectral mea- sure, non-commutative integration Mathematics Subject Classification 2010: 30G35, 17A05, 17A70, 47A10, 47L30, 47L60 1 operators was described [18, 19, 20, 21, 22]. Some results on their applications in partial differential equations were obtained [23, 24, 25, 26, 27]. This work continuous previous articles and uses their results. The present paper is devoted to unbounded normal operators and affiliated operators in octonion Hilbert spaces, that was not yet studied before.
[Show full text]