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79
A new entanglement measure induced by the HilbertSchmidt norm
 Phys.Lett. A
, 1998
"... In this letter we discuss new entanglement measure. It is based on the HilbertSchmidt norm... ..."
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In this letter we discuss new entanglement measure. It is based on the HilbertSchmidt norm...
Measuring statistical dependence with HilbertSchmidt norms
 PROCEEDINGS ALGORITHMIC LEARNING THEORY
, 2005
"... We propose an independence criterion based on the eigenspectrum of covariance operators in reproducing kernel Hilbert spaces (RKHSs), consisting of an empirical estimate of the HilbertSchmidt norm of the crosscovariance operator (we term this a HilbertSchmidt Independence Criterion, or HSIC). Th ..."
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Cited by 157 (43 self)
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We propose an independence criterion based on the eigenspectrum of covariance operators in reproducing kernel Hilbert spaces (RKHSs), consisting of an empirical estimate of the HilbertSchmidt norm of the crosscovariance operator (we term this a HilbertSchmidt Independence Criterion, or HSIC
gFrames and HilbertSchmidt operators
 Bull. Iran. Math. Soc
"... Abstract. In this paper we introduce and study Besselian gframes. We show that the kernel of associated synthesis operator for a Besselian gframe is finite dimensional. We also introduce αdual of a gframe and we get some results when we use the HilbertSchmidt norm for the members of a gframe ..."
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Abstract. In this paper we introduce and study Besselian gframes. We show that the kernel of associated synthesis operator for a Besselian gframe is finite dimensional. We also introduce αdual of a gframe and we get some results when we use the HilbertSchmidt norm for the members of a g
Some inequalities for unitarily invariant norms
 J. Math. Inequal
"... Abstract. This paper aims to present some inequalities for unitarily invariant norms. In section 2, we give a refinement of the CauchySchwarz inequality for matrices. In section 3, we obtain an improvement for the result of Bhatia and Kittaneh [Linear Algebra Appl. 308 (2000) 203211]. In section ..."
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4, we establish an improved Heinz inequality for the HilbertSchmidt norm. Finally, we present an inequality involving positive definite matrix and HilbertSchmidt norm. Then we use it to discuss the conjecture on the HilbertSchmidt norm of matrices proposed by Sloane and Harwit and the conjecture
IMPROVED YOUNG AND HEINZ INEQUALITIES WITH THE KANTOROVICH CONSTANT
, 2016
"... Abstract. In this article, we study the further refinements and reverses of the Young and Heinz inequalities with the Kantorovich constant. These modified inequalities are used to establish corresponding operator inequalities on a Hilbert space and HilbertSchmidt norm inequalities. ..."
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Abstract. In this article, we study the further refinements and reverses of the Young and Heinz inequalities with the Kantorovich constant. These modified inequalities are used to establish corresponding operator inequalities on a Hilbert space and HilbertSchmidt norm inequalities.
Entanglement measures and the HilbertSchmidt distance”, Phys
 Lett. A
"... In order to construct a measure of entanglement on the basis of a “distance ” between two states, it is one of desirable properties that the “distance ” is nonincreasing under every completely positive trace preserving map. Contrary to a recent claim, this letter shows that the HilbertSchmidt dista ..."
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distance does not have this property. PACS: 03.67a Keywords: entanglement; completely positive maps; operations; HilbertSchmidt norm As classical information arises from probability correlation between two random variables, quantum information arises from entanglement [1, 2]. Motivated by the finding
A COMPLETELY BOUNDED VIEW OF HILBERTSCHMIDT OPERATORS
"... Abstract. In this paper we make a separable infinite dimensional Hilbert space into a matricially norreed space in two ways, resulting in two matricially norreed spaces 7•1 and 792. We then prove that the completely bounded maps from •'•1 into 792 are the HilbertSchmidt operators, and that th ..."
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, and that the cbnorm is equal to the HilbertSchmidt norm. This result is then applied to characterize the matricial norm structure of 7•operator spaces. 1. Preliminaries. In this section we collect the basic facts and terminology needed for the exposition of our results. A very readable paper that develops
Bounds for linear multitask learning
 Journal of Machine Learning Research
, 2006
"... Abstract. We give dimensionfree and datadependent bounds for linear multitask learning where a common linear operator is chosen to preprocess data for a vector of task speci…c linearthresholding classi…ers. The complexity penalty of multitask learning is bounded by a simple expression involvin ..."
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Cited by 39 (9 self)
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involving the margins of the taskspeci…c classi…ers, the HilbertSchmidt norm of the selected preprocessor and the HilbertSchmidt norm of the covariance operator for the total mixture of all task distributions, or, alternatively, the Frobenius norm of the total Gramian matrix for the data
OPERATORLIPSCHITZ ESTIMATES FOR THE SINGULAR VALUE FUNCTIONAL CALCULUS
"... Abstract. We consider a functional calculus for compact operators, acting on the singular values rather than the spectrum, which appears frequently in applied mathematics. Necessary and sufficient conditions for this singular value functional calculus to be Lipschitzcontinuous with respect to the H ..."
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to the HilbertSchmidt norm are given. We also provide sharp constants. 1.
On finiteness of the sum of negative eigenvalues of Schrödinger operators
, 802
"... We prove conditions on potentials V which imply that the sum of the negative eigenvalues of the Schrödinger operator − ∆ + V is finite. We use a method for bounding eigenvalues based on estimates of the HilbertSchmidt norm of semigroup differences and on complex analysis. 1 ..."
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We prove conditions on potentials V which imply that the sum of the negative eigenvalues of the Schrödinger operator − ∆ + V is finite. We use a method for bounding eigenvalues based on estimates of the HilbertSchmidt norm of semigroup differences and on complex analysis. 1
Results 1  10
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79