论文标题
Birkhoff的延伸 - 半希尔伯特太空运营商的詹姆斯正交关系
An extension of Birkhoff--James orthogonality relations in semi-Hilbertian space operators
论文作者
论文摘要
令$ \ mathbb {b}（\ Mathcal {h}）$表示$ c^{\ ast} $ - Hilbert Space $ \ big \ big（\ Mathcal {h}，\ langle \ langle \ cdot，\ cdot，\ cdot \ cdot \ rangle \ rangle \ big big big）$ c^{\ ast {h}）$。给定一个正算子$ a \ in \ b（\ h）$，在[0,1] $中给定数字$λ\，一个seminorm $ {\ | \ cdot \ |} _ {（a，λ）} $定义在集合上$ \ b_ {a^a^a^{1/2}} $ and Ans $ Ane Ane Ane Ane Ane Ane Ane Ane Ane Ane Ane Ane Ane Ane AN $ a^{1/2} $ - 伴随。 seminorm $ {\ | \ cdot \ |} _ {（a，λ）} $是sesquilinear形式的组合，$ {\ langle \ cdot，\ cdot \ cdot \ rangle} _a $及其诱导的seminorm $ {伯克霍夫（Birkhoff）的表征 - 詹姆斯（James）在讨论的eminorm方面对操作员的正交性。 Moving $λ$ along the interval $[0,1]$, a wide spectrum of seminorms are obtained, having the $A$-numerical radius $w_A(\cdot)$ at the beginning (associated with $λ=0$) and the $A$-operator seminorm ${\|\cdot\|}_A$ at the end (associated with $λ=1$).此外，如果$ a = i $ the Identity运算符，则获得经典运算符的标准和数值半径。因此，本文的结果是该领域已知结果的显着扩展和概括。
Let $\mathbb{B}(\mathcal{H})$ denote the $C^{\ast}$-algebra of all bounded linear operators on a Hilbert space $\big(\mathcal{H}, \langle\cdot, \cdot\rangle\big)$. Given a positive operator $A\in\B(\h)$, and a number $λ\in [0,1]$, a seminorm ${\|\cdot\|}_{(A,λ)}$ is defined on the set $\B_{A^{1/2}}(\h)$ of all operators in $\B(\h)$ having an $A^{1/2}$-adjoint. The seminorm ${\|\cdot\|}_{(A,λ)}$ is a combination of the sesquilinear form ${\langle \cdot, \cdot\rangle}_A$ and its induced seminorm ${\|\cdot\|}_A$. A characterization of Birkhoff--James orthogonality for operators with respect to the discussed seminorm is given. Moving $λ$ along the interval $[0,1]$, a wide spectrum of seminorms are obtained, having the $A$-numerical radius $w_A(\cdot)$ at the beginning (associated with $λ=0$) and the $A$-operator seminorm ${\|\cdot\|}_A$ at the end (associated with $λ=1$). Moreover, if $A=I$ the identity operator, the classical operator norm and numerical radius are obtained. Therefore, the results in this paper are significant extensions and generalizations of known results in this area.
