### When may two systems of orthonormal functions be interchanged in vector-valued orthogonal sums?

#### Abstract

Given a finite orthonormal sequence(Error rendering LaTeX formula) in some and vectors in some Banach space X we are interested in the norm of the sums(Error rendering LaTeX formula) in .A constuction in [1] suggests that the system may be replaced by the set(Error rendering LaTeX formula) of coordinate functions(Error rendering LaTeX formula) on viewed as un orthonormal system with respect to a suitable measure λ on .We show by a convolutional argument that after symmetrization the measure λ is uniquely determined.We also discuss related questions.

DOI Code:
10.1285/i15900932v16n1p47

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