Abstract
We construct a countable algebraic basis of the algebra of all symmetric continuous polynomials on the Cartesian product ℓp1×…×ℓpn, where p1,…,pn∈[1,+∞), and ℓp is the complex Banach space of all p-power summable sequences of complex numbers for p∈[1,+∞).
Highlights
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In [14], the authors constructed an algebraic basis of the algebra of symmetric continuous complex-valued polynomials on the complex Banach space L∞ [0, 1] of complexvalued Lebesgue measurable essentially bounded functions on [0, 1]
This result gave us the opportunity to describe the spectrum of the Fréchet algebra Hbs ( L∞ [0, 1]) of symmetric analytic entire functions, which are bounded on bounded sets on the complex Banach space L∞ [0, 1] and to show that the algebra Hbs ( L∞ [0, 1])
Summary
In [14], the authors constructed an algebraic basis of the algebra of symmetric continuous complex-valued polynomials on the complex Banach space L∞ [0, 1] of complexvalued Lebesgue measurable essentially bounded functions on [0, 1] This result gave us the opportunity to describe the spectrum of the Fréchet algebra Hbs ( L∞ [0, 1]) of symmetric analytic entire functions, which are bounded on bounded sets on the complex Banach space L∞ [0, 1] (see [14]) and to show that the algebra Hbs ( L∞ [0, 1]). In [46] there was constructed a countable algebraic basis of the algebra of all symmetric continuous complex-valued polynomials on the Cartesian power of the complex Banach spacep. This result was generalized to the real case in [47].
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