Spectral measures, boundedly $\sigma$-complete Boolean algebras and applications to operator theory
نویسندگان
چکیده
منابع مشابه
BOUNDEDLY a-COMPLETE BOOLEAN ALGEBRAS AND APPLICATIONS TO OPERATOR THEORY
A systematic study is made of spectral measures in locally convex spaces which are countably additive for the topology of uniform convergence on bounded sets, briefly, the bounded convergence topology. Even though this topology is not compatible for the duality with respect to the pointwise convergence topology it turns out, somewhat surprisingly, that the corresponding L'-spaces for the spectr...
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Let B be a complete ccc Boolean algebra and let τs be the topology on B induced by the algebraic convergence of sequences in B. 1. Either there exists a Maharam submeasure on B or every nonempty open set in (B, τs) is topologically dense. 2. It is consistent that every weakly distributive complete ccc Boolean algebra carries a strictly positive Maharam submeasure. 3. The topological space (B, τ...
متن کاملComplete Quotient Boolean Algebras
For I a proper, countably complete ideal on P(X) for some set X , can the quotient Boolean algebra P(X)/I be complete? This question was raised by Sikorski [Si] in 1949. By a simple projection argument as for measurable cardinals, it can be assumed that X is an uncountable cardinal κ, and that I is a κ-complete ideal on P(κ) containing all singletons. In this paper we provide consequences from ...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1987
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1987-0911097-2