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Sums of commutators in ideals and modules of type II factors

Kenneth J. Dykema, Nigel J. Kalton (2005)

Annales de l’institut Fourier

Let be a factor of type II or II 1 having separable predual and let ¯ be the algebra of affiliated τ -measurable operators. We characterize the commutator space [ , 𝒥 ] for sub- ( , ) - bimodules and 𝒥 of ¯ .

Sums of commuting operators with maximal regularity

Christian Le Merdy, Arnaud Simard (2001)

Studia Mathematica

Let Y be a Banach space and let S L p be a subspace of an L p space, for some p ∈ (1,∞). We consider two operators B and C acting on S and Y respectively and satisfying the so-called maximal regularity property. Let ℬ and be their natural extensions to S ( Y ) L p ( Y ) . We investigate conditions that imply that ℬ + is closed and has the maximal regularity property. Extending theorems of Lamberton and Weis, we show in particular that this holds if Y is a UMD Banach lattice and e - t B is a positive contraction on L p for any...

Super real closed rings

Marcus Tressl (2007)

Fundamenta Mathematicae

A super real closed ring is a commutative ring equipped with the operation of all continuous functions ℝⁿ → ℝ. Examples are rings of continuous functions and super real fields attached to z-prime ideals in the sense of Dales and Woodin. We prove that super real closed rings which are fields are an elementary class of real closed fields which carry all o-minimal expansions of the real field in a natural way. The main part of the paper develops the commutative algebra of super real closed rings, by...

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