Semi-regular biorthogonal pairs and generalized Riesz bases

H. Inoue
2016 Journal of Mathematical Physics  
In this paper we define the notion of semi-regular biorthogonal pairs what is a generalization of regular biorthogonal pairs in Ref. hiroshi1 and show that if ({ϕ_n} , {ψ_n}) is a semi-regular biorthogonal pair, then {ϕ_n} and {ψ_n} are generalized Riesz bases. This result improves the results of Ref. h-t, hiroshi1, h-t2 in the regular case.
doi:10.1063/1.4966927 fatcat:rboiqysccvd77erzvnendskkye