Abstract Harmonic Analysis

Hewitt, Edwin; Ross, Kenneth A.

doi:10.1007/978-3-662-00102-8

Cited by 443 publications

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“…The properties of amenable semigroups and invariant means on them can be found, for example, in [120], [121]; in particular, it is known that a commutative semigroup is amenable. We shall say that problem (6.6) is invariant, or more precisely, (Θ, T)-invariant, if, for any (x, y) G W and s G 5, there exists an element y' £Y with the properties y = r(s)y', (9(s) and in problem (6.6) there exists an extremal operator that is (Τ, Θ)-invariant.…”

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confidence: 99%

Approximation of unbounded operators by bounded operators and related extremal problems

Arestov¹

1996

Russ. Math. Surv.

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confidence: 99%

Approximation of unbounded operators by bounded operators and related extremal problems

Arestov¹

1996

Russ. Math. Surv.

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“…If two or more terms of this sort were present, then the decomposition of f would contain at least two terms from W k by virtue of step 2, which contradicts the condition. 7. The decomposition of f 1 contains only one term from W k < .…”

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Arithmetic of semigroups of series in multiplicative systems

Il’inskaya¹

2009

Ukr Math J

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Il'inskaya UDC 519.21 We study the arithmetic of a semigroup M P of functions with operation of multiplication representable in the form f x a x n n n ( ) ( ) = = ∞ ∑ χ 0 a a n n n ≥ = = ∞ ∑ ( ) 0 1 0 , , where { } χ n n= ∞ 0 is a system of multiplicative functions that are generalizations of the classical Walsh functions. For the semigroup M P , analogs of the well-known Khinchin theorems related to the arithmetic of a semigroup of probability measures in R n are true. We describe the class I 0 ( ) M P of functions without indivisible or nondegenerate idempotent divisors and construct a class of indecomposable functions that is dense in M P in the topology of uniform convergence.

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“…If S is only left cancellative, then (4) implies (1) provided F -B(S) (see [8,Theorem 17.15 (iii) implies (i)]). Theorem 3.6.…”

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“…Using Theorem 3.1 and the arguments used in Granirer [6, Lemma 3, p. 99] we obtain the implications (1) => (2) => (3) => (4). For (3) => (1), we use Theorem 3.1 again and the arguments in Hewitt and Ross [8,Theorem 17.15,p. 235].…”

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On left thickness of subsets in semigroups

Wong¹

1982

Proc. Amer. Math. Soc.

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Abstract. We reformulate the concept of left thickness in a semigroup introduced by H. Junghenn in Amenability of function spaces on thick subsemigroups, Proc. Amer.Math. Soc. 75 (1979), 37-41, and obtain a number of interesting new characterisations of left thickness without assuming left amenability. Moreover, these characterisations are similar in nature to familiar characterisations of left amenability on semigroups. We also sharpen some of Junghenn's results, paving the way for extension to locally compact semigroups.

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Abstract Harmonic Analysis

Cited by 443 publications

References 0 publications

Approximation of unbounded operators by bounded operators and related extremal problems

Approximation of unbounded operators by bounded operators and related extremal problems

Arithmetic of semigroups of series in multiplicative systems

On left thickness of subsets in semigroups

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