极分解定理的注记
A Note on the Polar Decomposition Theorem
设H和K是Hilbert空间.首先,对给定的算子T∈B(H,K),刻画了集合UT={U∈B(H,K):U是部分等距算子并且T=U(T*T)1/2}. 其次,对部分等距算子U∈B(H,K),还给出集合TU={T∈B(H,K):N(T)=N(U),R(T)=R(U),T=U(T*T)1/2}的刻画. 最后,作为主要结果的应用得到了相关结论.
Let H and K be Hilbert spaces. For given T ∈ B(H, K), the set UT={U ∈ B(H, K):U is a partial isometry and T=U(T*T)1/2} is characterized, and then it is also given that a characterization of TU={T ∈ B(H, K):N (T)=N (U), R(T)=R(U), T=U(T*T) 2/1 } for some partial isometry U ∈ B(H, K). In addition, as applications of the main results, some related results are obtained.
算子矩阵 / 极分解 / hypo-EP算子 / Moore-Penreso逆 {{custom_keyword}} /
operator matrices / polar decomposition / hypo-EP operator / Moore–Penreso inverse {{custom_keyword}} /
[1] Andruchow E., Classes of idempotents in Hilbert space, Complex Anal. Oper. Theory, 2016, 10:1383-1409.
[2] Baksalary O. M., Styan G. P. H., Trenkler G., On a matrix decomposition of Hartwig and Spindelböck, Linear Algebra Appl., 2009, 430:2798-2812.
[3] Baksalary O. M., Trenkler G., Core inverse of matrices, Linear Multilinear Algebra, 2010, 58:681-697.
[4] Baksalary O. M., Trenkler G., On the projectors F F† and F†F, Appl. Math. Comput., 2011, 217:10213-10223.
[5] Baksalary O. M., Trenkler G., On disjoint range matrices, Linear Algebra Appl., 2011, 435:1222-1240.
[6] Ben-Israel A., Greville T. N. E., Generalized Inverses:Theory and Applications, Second Edition, SpringerVerlag, New York, 2003.
[7] Benítez J., Rakocevic V., Matrices A such that AA† -A†A are nonsingular, Appl. Math. Comput., 2010, 217:3493-3503.
[8] Benítez J., Rakocevic V., Canonical angles and limits of sequences of EP and co-EP matrices, Appl. Math. Comput., 2012, 218:8503-8512.
[9] Conway J. B., A Course in Functional Analysis, Springer-Verlag, New York, 1990.
[10] Corach G., Maestripier A., Polar decomposition of oblique projections, Linear Algebra Appl., 2010, 433:511-519.
[11] Drivaliaris D., Karanasios S., Pappas D., Factorizations of EP operators, Linear Algebra Appl., 2008, 429:1555-1567.
[12] Hartwig R. E., Spindelböck K., Matrices for which A* and A† commute, Linear Multilinear Algebra, 1984, 14:241-256.
[13] Ichinose W., Iwashita K., On the uniqueness of the polar decomposition of bounded operators in Hilbert spaces, J. Operator Theory, 2013, 70:175-180.
[14] Itoh M., On some EP operators, Nihonkai Math. J., 2005, 16:49-56.
[15] Kubrusly C. S., Elements of Operator Theory, Birkhäuser, Boston, 2001.
国家自然科学基金资助项目(11761052,11761029);内蒙古自然科学基金资助项目(2015MS0117)
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