Inhaltszusammenfassung

Given Banach spaces X and Y, we show that, for each operator-valued analytic map alpha is an element of O(D, L(Y, X)) satisfying the finiteness condition dim(X/alpha(z)Y) < 8 pointwise on an open set D in C(n), the induced multiplication operator O(U,Y) ->alpha O(U, X) has closed range on each Stein open set U subset of D. As an application we deduce that the generalized range R(infinity)(T) = boolean AND(k >= 1) Sigma(|alpha|=kappa) T(alpha) X of a commuting multioperator T is an element of ...Given Banach spaces X and Y, we show that, for each operator-valued analytic map alpha is an element of O(D, L(Y, X)) satisfying the finiteness condition dim(X/alpha(z)Y) < 8 pointwise on an open set D in C(n), the induced multiplication operator O(U,Y) ->alpha O(U, X) has closed range on each Stein open set U subset of D. As an application we deduce that the generalized range R(infinity)(T) = boolean AND(k >= 1) Sigma(|alpha|=kappa) T(alpha) X of a commuting multioperator T is an element of L(X)(n) with dim(X/Sigma(n)(i=1) T(i)X) < infinity can be represented as a suitable spectral subspace. » weiterlesen» einklappen

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