Results 71 to 80 of about 865 (99)
Higher-rank numerical range in infinite-dimensional Hilbert space
, 2008 In this paper we calculate the higher-rank numerical range, as defined by Choi, Kribs and . Zyczkowski, of selfadjoint operators and of nonunitary isometries on infinite-dimensional Hilbert space.
R. Martínez-Avendaño
semanticscholar +1 more source
Partial Inner Products on Antiduals [PDF]
arXiv, 2017 We discuss extensions of an inner product from a vector space to its full antidual. None of these extensions is weakly continuous, but partial extensions recapture some familiar structure including the Hilbert space completion and the antiduality pairing.
arxiv
A note on the maximal numerical range [PDF]
arXiv, 2018 We show that the maximal numerical range of an operator has a non-empty intersection with the boundary of its numerical range if and only if the operator is normaloid. A description of this intersection is also given.
arxiv
A Lebesgue-type decomposition on one side for sesquilinear forms [PDF]
arXiv, 2019 Sesquilinear forms which are not necessarily positive may have a different behavior, with respect to a positive form, on each side. For this reason a Lebesgue-type decomposition on one side is provided for generic forms satisfying a boundedness condition.
arxiv
Some inequalities for $(\alpha, \beta)$-normal operators in Hilbert spaces
, 2008 An operator $T$ acting on a Hilbert space is called $(\alpha ,\beta)$-normal ($0\leq \alpha \leq 1\leq \beta $) if \begin{equation*} \alpha ^{2}T^{\ast }T\leq TT^{\ast}\leq \beta ^{2}T^{\ast}T.
Dragomir, Sever S. +1 more
core
A Note Around Operator Bellman Inequality [PDF]
arXiv, 2019 In this paper, we shall give an extension of operator Bellman inequality. This result is estimated via Kantorovich constant.
arxiv
On the higher rank numerical range of the shift operator
, 2010 For any n-by-n complex matrix T and any $1\leqslant k\leqslant n$, let $\Lambda_{k}(T)$ the set of all $\lambda\in \C$ such that $PTP=\lambda P$ for some rank-k orthogonal projection $P$ be its higher rank-k numerical range. It is shown that if $\bbS$ is
Gaaya, Haykel
core +1 more source
The Alternative Daugavet Property of $C^*$-algebras and $JB^*$-triples [PDF]
arXiv, 2004 A Banach space $X$ is said to have the alternative Daugavet property if for every (bounded and linear) rank-one operator $T:X\longrightarrow X$ there exists a modulus one scalar $\omega$ such that $\|Id + \omega T\|= 1 + \|T\|$. We give geometric characterizations of this property in the setting of $C^*$-algebras, $JB^*$-triples and their isometric ...
arxiv
New Reverse Inequalities for the Numerical Radius of Normal Operators in Hilbert Spaces [PDF]
arXiv, 2005 In this paper, more inequalities between the operator norm and its numerical radius, for the class of normal operators, are established. Some of the obtained results are based on recent reverse results for the Schwarz inequality in Hilbert spaces due to the author.
arxiv
A characterization of The operator-valued triangle equality [PDF]
arXiv, 2005 We will show that for any two bounded linear operators $X,Y$ on a Hilbert space ${\frak H}$, if they satisfy the triangle equality $|X+Y|=|X|+|Y|$, there exists a partial isometry $U$ on ${\frak H}$ such that $X=U|X|$ and $Y=U|Y|$. This is a generalization of Thompson's theorem to the matrix case proved by using a trace.
arxiv