WebA bounded operator Ais Hilbert-Schmidt if P j 1 kAe jk 2 <1for some (any) Hilbert basis (e j) j 1. The space of Hilbert-Schmidt operators is also a Hilbert space (a fact which will be a key in our development) endowed with the scalar product hA;Bi HS = P j hAe j;Be ji and we denote by kk HS): WebOct 20, 2016 · Hilbert-Schmidt Theory Symmetric Kernel Complete Orthonormal System Orthogonalization Process Expansion Theorem These keywords were added by machine …

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WebSome remarks rather than an answer: A may be only densely defined and unbounded, hence may not be Hilbert-Schmidt. But rather the inverse of A is compact. Moreover, coercivity guaranttes that the inverse of A is bounded, then you apply the H-S theorem. http://web.mit.edu/lrosasco/www/publications/operator_estimates.pdf from which book jee questions are taken

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WebWe propose an independence criterion based on the eigenspectrum of covariance operators in reproducing kernel Hilbert spaces (RKHSs), consisting of an empirical estimate of the Hilbert-Schmidt norm of the cross-covariance operator (we term this a Hilbert-Schmidt Independence Criterion, or HSIC). The Hilbert–Schmidt operators form a two-sided *-ideal in the Banach algebra of bounded operators on H. They also form a Hilbert space, denoted by BHS(H) or B2(H), which can be shown to be naturally isometrically isomorphic to the tensor product of Hilbert spaces where H∗ is the dual space of H. See more In mathematics, a Hilbert–Schmidt operator, named after David Hilbert and Erhard Schmidt, is a bounded operator $${\displaystyle A\colon H\to H}$$ that acts on a Hilbert space $${\displaystyle H}$$ and … See more • Every Hilbert–Schmidt operator T : H → H is a compact operator. • A bounded linear operator T : H → H is Hilbert–Schmidt if and only if the same … See more • Frobenius inner product • Sazonov's theorem • Trace class – compact operator for which a finite trace can be defined See more An important class of examples is provided by Hilbert–Schmidt integral operators. Every bounded operator with a finite-dimensional range (these are called operators of finite … See more The product of two Hilbert–Schmidt operators has finite trace-class norm; therefore, if A and B are two Hilbert–Schmidt operators, the Hilbert–Schmidt inner product can be defined as The Hilbert–Schmidt … See more http://www.southerndays.info/Starling/Adam_Starling_notes.html ghostbusters eaglemoss