"Growth Conditions and Inverse Producing Extensions"@en . "P(GA201/03/0041), Z(AV0Z10190503)" . . "2"^^ . . . "0379-4024" . "1"^^ . "We study the invertibility of Banach algebras elements in their extensions, and invertible extensions of Banach and Hilbert space operators with prescribed growth conditions for the norm of inverses. As applications, the solutions of two open problems are obtained. In the first one we give a characterization of .epsilon.(T)-subscalar operators in terms of growth conditions. In the second one we show that operators satisfying a Beurling-type growth condition possess Bishop\u00B4s property (.beta.). Other applications are also given."@en . . . . . . "M\u00FCller, Vladim\u00EDr" . "[A7EFFEC7C1E3]" . . "RO - Rumunsko" . "RIV/67985840:_____/05:00031544!RIV06-AV0-67985840" . "25"^^ . . . "522956" . . . "We study the invertibility of Banach algebras elements in their extensions, and invertible extensions of Banach and Hilbert space operators with prescribed growth conditions for the norm of inverses. As applications, the solutions of two open problems are obtained. In the first one we give a characterization of .epsilon.(T)-subscalar operators in terms of growth conditions. In the second one we show that operators satisfying a Beurling-type growth condition possess Bishop\u00B4s property (.beta.). Other applications are also given." . "Jsou charakterizov\u00E1ny .epsilon.(T)-substal\u00E1rn\u00ED oper\u00E1tory pomoc\u00ED r\u016Fstu mocnin. D\u00E1le je uk\u00E1z\u00E1no, \u017Ee oper\u00E1tory spl\u0148uj\u00EDc\u00ED Beurlingovu podm\u00EDnku maj\u00ED Bishopovu vlastnost (.beta.)."@cs . "415;439" . . "1" . "Growth Conditions and Inverse Producing Extensions"@en . "invertible extensions; growth conditions; subscalar operators"@en . "Journal of Operator Theory" . "RIV/67985840:_____/05:00031544" . "Podm\u00EDnky na r\u016Fst a roz\u0161\u00ED\u0159en\u00ED zaji\u0161\u0165uj\u00EDc\u00ED invertibilitu"@cs . . "Growth Conditions and Inverse Producing Extensions" . "Growth Conditions and Inverse Producing Extensions" . . "Podm\u00EDnky na r\u016Fst a roz\u0161\u00ED\u0159en\u00ED zaji\u0161\u0165uj\u00EDc\u00ED invertibilitu"@cs . "54" . . "Badea, C." .