Titlebook: Introduction to Operator Theory in Riesz Spaces; Adriaan C. Zaanen Book 1997 Springer-Verlag Berlin Heidelberg 1997 Boolean algebra.Calc.E

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Complex Riesz Spaces,ture by defining.and the so defined complex vector space is denoted by . + .. Note that (.,0) + (.,0) = (. + .,0) and .(.,0)=(.,0) for α real. Hence, identifying . ∈ . and (.,0)∈ . + ., the space . is embedded in . + . as a real-linear subspace. Note also that .(., 0) = (0, .) by the above definition, so

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Riesz Spaces,as scalar multipliers by .,… (this choice for the notation is related to the fact that in many examples the space consists of realvalued functions). The null element (zero element, neutral element) with respect to addition will be denoted by 0; it will always be clear whether we speak about the null element or about the number zero.

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Linear Operators, operator. It is evident that the set . (.) of all operators from . into . is a vector space if, for ., . in . ( .) and . real or complex, we define . + . by. If ., ., . are vector spaces and ., . are operators such that .: . →. and .: . → ., then the product operator . : . → . is defined by

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Book 1997H. Stone on Hilbert spaces and by S. Banach on linear operators, both from 1932. The amount of material in the field of functional analysis (in­ cluding operator theory) has grown to such an extent that it has become impossible now to include all of it in one book. This holds even more for text­ boo