Abstract
We generalize the notion of the numerical range in such a way that the ranges of elements of a given normed algebra are sets of elements of some other normed algebra, and that the states are linear operators. We show that many properties of numerical range rest unchanged, including the connection between range and spectrum. For Hermitian elements we deduce Vidav’s lemma and associator identities [x, x, x] = [x, x 2, x] = 0.
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© 1994 Springer Science+Business Media Dordrecht
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Cedilnik, A. (1994). Ranges of Elements of a Nonassociative Algebra. In: González, S. (eds) Non-Associative Algebra and Its Applications. Mathematics and Its Applications, vol 303. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0990-1_15
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DOI: https://doi.org/10.1007/978-94-011-0990-1_15
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-4429-5
Online ISBN: 978-94-011-0990-1
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