Displaying similar documents to “Theory of the integral”

α-Equivalence

Kyewon Koh Park (1998)

Studia Mathematica

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We define the α - relations between discrete systems and between continuous systems. We show that it is an equivalence relation. α- Equivalence vs. even α-equivalence is analogous to Kakutani equivalence vs. even Kakutani equivalence.

Factorization through Hilbert space and the dilation of L(X,Y)-valued measures

V. Mandrekar, P. Richard (1993)

Studia Mathematica

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We present a general necessary and sufficient algebraic condition for the spectral dilation of a finitely additive L(X,Y)-valued measure of finite semivariation when X and Y are Banach spaces. Using our condition we derive the main results of Rosenberg, Makagon and Salehi, and Miamee without the assumption that X and/or Y are Hilbert spaces. In addition we relate the dilation problem to the problem of factoring a family of operators through a single Hilbert space.

Measures and lacunary sets

Pascal Lefèvre (1999)

Studia Mathematica

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We establish new connections between some classes of lacunary sets. The main tool is the use of (p,q)-summing or weakly compact operators (for Riesz sets). This point of view provides new properties of stationary sets and allows us to generalize to more general abelian groups than the torus some properties of p-Sidon sets. We also construct some new classes of Riesz sets.

One-parameter subgroups and the B-C-H formula

Wojciech Wojtyński (1994)

Studia Mathematica

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An algebraic scheme for Lie theory of topological groups with "large" families of one-parameter subgroups is proposed. Such groups are quotients of "𝔼ℝ-groups", i.e. topological groups equipped additionally with the continuous exterior binary operation of multiplication by real numbers, and generated by special ("exponential") elements. It is proved that under natural conditions on the topology of an 𝔼ℝ-group its group multiplication is described by the B-C-H formula in terms of the...