$$(\alpha ,\beta )$$(α,β)-A-Normal operators in semi-Hilbertian spaces
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DOI: 10.1007/s13370-019-00690-3
Abstract: Let $${\mathcal {H}}$$H be a Hilbert space and let A be a positive bounded operator on $${\mathcal {H}}$$H. The semi-inner product $$\langle u\;|\;v \rangle _A:=\langle Au\;|\;v\rangle ,\;\;u,v \in {\mathcal {H}}$$⟨u|v⟩A:=⟨Au|v⟩,u,v∈H induces a semi-norm $$\left\| .\;\right\|… read more here.
Keywords: beta normal; normal operators; operators semi; semi hilbertian ... See more keywords
(A, m)-Isometric Unilateral Weighted Shifts in Semi-Hilbertian Spaces
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DOI: 10.1007/s40840-016-0307-5
Abstract: For a positive integer m, a bounded linear operator T on a Hilbert space $$\mathbb {H}$$H is called an (A, m)-isometry, if $$\Theta ^{(m)}_{A}(T) =\sum _{k=0}^{m}(-1)^{m-k}{m\atopwithdelims ()k}T^{*k}AT^{k}=0$$ΘA(m)(T)=∑k=0m(-1)m-kmkT∗kATk=0, where A is a positive (semi-definite) operator. In this… read more here.
Keywords: unilateral weighted; isometric unilateral; weighted shifts; shifts semi ... See more keywords