부산대학교 도서관

A m-quasi class AkM∈Q(Ak,m)HM∗m|Mk+1|2k+1Mm≥M∗m|M|2Mm,λM∈Q(Ak,m)M⊗NQAk, denoted as AkM∈Q(Ak,m)HM∗m|Mk+1|2k+1Mm≥M∗m|M|2Mm,λM∈Q(Ak,m)M⊗NQAk, is defined as an operator M acting on a complex Hilbert space AkM∈Q(Ak,m)HM∗m|Mk+1|2k+1Mm≥M∗m|M|2Mm,λM∈Q(Ak,m)M⊗NQAk, provided that the following condition holds true: AkM∈Q(Ak,m)HM∗m|Mk+1|2k+1Mm≥M∗m|M|2Mm,λM∈Q(Ak,m)M⊗NQAkwhere both k and m are positive integers. In this research, we unveil fundamental structural characteristics of these operators. Leveraging these findings, we can establish that P is self-adjoint if P represents the Riesz idempotent associated with the isolated point AkM∈Q(Ak,m)HM∗m|Mk+1|2k+1Mm≥M∗m|M|2Mm,λM∈Q(Ak,m)M⊗NQAk in the spectrum of AkM∈Q(Ak,m)HM∗m|Mk+1|2k+1Mm≥M∗m|M|2Mm,λM∈Q(Ak,m)M⊗NQAk. Additionally, we provide a necessary and sufficient condition for AkM∈Q(Ak,m)HM∗m|Mk+1|2k+1Mm≥M∗m|M|2Mm,λM∈Q(Ak,m)M⊗NQAk to belong to AkM∈Q(Ak,m)HM∗m|Mk+1|2k+1Mm≥M∗m|M|2Mm,λM∈Q(Ak,m)M⊗NQAk when both M and N are non-zero.