Angles and Schauder basis in Hilbert spaces

2018/06/20 by Hou, Bingzhe, Cao, Yang, Tian, Geng +1
#47B37 #FOS: Mathematics #Functional Analysis (math.FA) #Primary 46B15 #Secondary 46B20

paper · doi:10.48550/arxiv.1806.07866

Abstract

Let H be a complex separable Hilbert space. We prove that if \f_n\_n=1^∞ is a Schauder basis of the Hilbert space H, then the angles between any two vectors in this basis must have a positive lower bound. Furthermore, we investigate that \z^σ^-1(n)\_n=1^∞ can never be a Schauder basis of L²(\mathbbT,ν), where \mathbbT is the unit circle, ν is a finite positive discrete measure, and σ: ℤ → ℕ is an arbitrary surjective and injective map.

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