Zeros of quadratic functionals on non-separable spaces
We construct non-separable subspaces in the kernel of every quadratic functional on some classes of complex and real Banach spaces.
Hilbert spaces of analytic functions of infinitely many variables
We study spaces of analytic functions generated by homogeneous polynomials from the dual space to the symmetric Hilbertian tensor product of a Hilbert space. In particular, we introduce an analogue of the classical Hardy space H² on the Hilbert unit ball and investigate spectral decomposition of unitary operators on this space. Also we prove a Wiener-type theorem for an algebra of analytic functions on the Hilbert unit ball.
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