$$(\alpha ,\beta )$$(α,β)-A-Normal operators in semi-Hilbertian spaces
Sign Up to like & getrecommendations! Published in 2019 at "Afrika Matematika"
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 $$\left\| .\;\right\|… read more here.
Keywords: beta normal; normal operators; operators semi; semi hilbertian ... See more keywords
(A, m)-Isometric Unilateral Weighted Shifts in Semi-Hilbertian Spaces
Sign Up to like & getrecommendations! Published in 2018 at "Bulletin of the Malaysian Mathematical Sciences Society"
DOI: 10.1007/s40840-016-0307-5
Abstract: For a positive integer m, a bounded linear operator T on a Hilbert space $$\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
A-numerical radius inequalities for semi-Hilbertian space operators
Sign Up to like & getrecommendations! Published in 2019 at "Linear Algebra and its Applications"
DOI: 10.1016/j.laa.2019.05.012
Abstract: Let $A$ be a positive bounded operator on a Hilbert space $\big(\mathcal{H}, \langle \cdot, \cdot\rangle \big)$. The semi-inner product ${\langle x, y\rangle}_A := \langle Ax, y\rangle$, $x, y\in\mathcal{H}$ induces a semi-norm ${\|\cdot\|}_A$ on $\mathcal{H}$. Let… read more here.
Keywords: numerical radius; space; semi hilbertian; hilbertian space ... See more keywords