Properties of restrictions of the operator of multiplication by a continuous function

• Date: 1995
• Main Authors: Shevchik, V. V., Шевчик, В. В.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 1995
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/5570
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

For the operatorA of multiplication by a continuous functiona (t) in the Hilbert spaceL 2[0, b]=H, we give a description of two sets of infinite-dimensional subspaces with infinite codimensions:I(A)={N⊂H:A/N is an isomorphism},K(A)={M⊂H: A/M is a compact mapping}. As an application, we consider the...