On the geometry in projective limits of Hilbert spaces

AbstractIn this paper we consider the concept of orthogonality with respect to infinitely many inner products. We describe geometric properties related to this concept of orthogonality in certain Köthe sequence spaces (power series spaces), spaces of holomorphic functions in one and several variables and spaces of infinitely differentiable functions. The methods are required from a mixture of functional analysis (theory of bases), theory of functions of one complex variable, Fourier analysis and interpolation theory