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Holomorphic kernels and commuting operators

Holomorphic kernels and commuting operators

Necessary and sufficient conditions in terms of operator polynomials are obtained for an <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="m"> <mml:semantics> <mml:mi>m</mml:mi> <mml:annotation encoding="application/x-tex">m</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-tuple <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper T equals left-parenthesis upper T 1 comma ellipsis comma upper T Subscript m Baseline right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mi>T</mml:mi> <mml:mo>=</mml:mo> <mml:mo …