Regularity of Banach algebras generated by analytic semigroups satisfying some growth conditions
Regularity of Banach algebras generated by analytic semigroups satisfying some growth conditions
We show that if a commutative complex Banach algebra <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper A"> <mml:semantics> <mml:mi>A</mml:mi> <mml:annotation encoding="application/x-tex">A</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is generated by a nonzero analytic semigroup <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis a Superscript t Baseline right-parenthesis upper R e t greater-than 0"> <mml:semantics> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mrow …