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Solved and unsolved problems in generalized notions of amenability for Banach algebras

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Zhang Y.

Banach Center Publications

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2010

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tom 91

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nr 1

441-454

EN

We survey the recent investigations on approximate amenability/contractibility and pseudo-amenability/contractibility for Banach algebras. We will discuss the core problems concerning these notions and address the significance of any solutions to them to the development of the field. A few new results are also included.

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Some observations on the Diophantine equation f(x)f(y) = f(z)²

100%

Zhang Y.

Colloquium Mathematicum

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2016

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tom 142

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nr 2

275-283

EN

Let f ∈ ℚ [X] be a polynomial without multiple roots and with deg(f) ≥ 2. We give conditions for f(X) = AX² + BX + C such that the Diophantine equation f(x)f(y) = f(z)² has infinitely many nontrivial integer solutions and prove that this equation has a rational parametric solution for infinitely many irreducible cubic polynomials. Moreover, we consider f(x)f(y) = f(z)² for quartic polynomials.

3

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Fixed point properties for semigroups of nonexpansive mappings on convex sets in dual Banach spaces

63%

Lau A. T.-M., Zhang Y.

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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2018

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tom 17

Ograniczanie wyników

1 Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

1 Banach Center Publications

1 Colloquium Mathematicum

3 Zhang Y.

1 Lau A. T.-M.

1 2018

1 2016

1 2010

Solved and unsolved problems in generalized notions of amenability for Banach algebras

Some observations on the Diophantine equation f(x)f(y) = f(z)²

Fixed point properties for semigroups of nonexpansive mappings on convex sets in dual Banach spaces