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Linear operations and functionals
18 other sections not shown
algebraic applying arbitrary assume B-space barrelled space bounded set bounded variation characteristic value closed set closure coefficients compact complex spaces conditions of Theorem consequently consider continuous function convex set Corollary corresponding defined definition denote dense denumerable derivative differentiable domain eigenvalue element equivalent exists fact finite-dimensional function of bounded fundamental system given Hence Hilbert space implies inequality interval kernel Lemma Let X0 limit linear functional linear inverse linear operation linear set linear topological space locally convex space matrix method metric space necessary and sufficient neighbourhood of zero Newton's method normed space notation obtain obviously operation mapping orthogonal point x0 polynomial Proof properties real numbers Remark right-hand side satisfying the condition self-adjoint operator sequence xn sphere subspace sufficient condition system of neighbourhoods tion topological space topology unique weak convergence weakly whence write