Compact covariance operators
نویسندگان
چکیده
منابع مشابه
Compact Sets and Compact Operators
Proof. Properties 2 and 3 are left to the reader. For property 1, assume that S is an unbounded compact set. Since S is unbounded, we may select a sequence {vn}n=1 such that ‖vn‖ → 0 as n→∞. Since S is compact, this sequence will have a convergent subsequence, say {vk}k=1, which will still be unbounded. This sequence is Cauchy, so there is a positive integer K for which ‖v`− vm‖ ≤ 1/2 for all `...
متن کاملCompact Operators
In these notes we provide an introduction to compact linear operators on Banach and Hilbert spaces. These operators behave very much like familiar finite dimensional matrices, without necessarily having finite rank. For more thorough treatments, see [RS, Y]. Definition 1 Let X and Y be Banach spaces. A linear operator C : X → Y is said to be compact if for each bounded sequence {xi}i∈IN ⊂ X , t...
متن کاملJoint Measures and Cross-covariance Operators Jon·it I"leasures and Cross-covariance Operators Joint L"leasljres and Cross-covariance Operators*
Let HI (resp., HZ) be a real and separable Hilbert space with Borel a-field f 1 (resp., f 2), and let (HIXH Z ' f 1 x f 2) be the product measurable space generated by the measurable rectangles. This paper develops relations between probability measures on (HIXH Z ' f 1 x f 2), i.e., joint measures, and the projections of such measures on (HI' f 1) and (HZ' f 2). In particular, the class of all...
متن کاملCompact Operators
In these notes we provide an introduction to compact linear operators on Banach and Hilbert spaces. These operators behave very much like familiar finite dimensional matrices, without necessarily having finite rank. For more thorough treatments, see [RS, Y]. Definition 1 Let X and Y be Banach spaces. A linear operator C : X → Y is said to be compact if for each bounded sequence {xi}i∈IN ⊂ X , t...
متن کاملCompact weighted Frobenius-Perron operators and their spectra
In this note we characterize the compact weighted Frobenius-Perron operator $p$ on $L^1(Sigma)$ and determine their spectra. We also show that every weakly compact weighted Frobenius-Perron operator on $L^1(Sigma)$ is compact.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1981
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1981-0627699-7