Abstract
The family of operators on a pip-space V is endowed with two, possibly different, partial multiplications, where partial means that the multiplication is not defined for any pair A,B of elements of Op(V) but only for certain couples. The two multiplications, to be called strong and weak, give rise to two different structures that coincide in certain situations. In this chapter we will discuss first the structure of Op(V) as partial *-algebra in the sense of [AIT02] and then the possibility of representing an abstract partial *-algebra into Op(V).
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© 2009 Springer-Verlag Berlin Heidelberg
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Antoine, JP., Trapani, C. (2009). Partial *-Algebras of Operators in a PIP-Space. In: Partial Inner Product Spaces. Lecture Notes in Mathematics(), vol 1986. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-05136-4_6
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DOI: https://doi.org/10.1007/978-3-642-05136-4_6
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-05135-7
Online ISBN: 978-3-642-05136-4
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