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

  • V. V. Shevchik

Abstract

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 problem of determining whether the sequence {a(t)en(t)}, where {en(t)} is an orthonormal basis in L2[0,b], is an unconditional basis.
Published
25.12.1995
How to Cite
ShevchikV. V. “Properties of Restrictions of the Operator of Multiplication by a Continuous Function”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 47, no. 12, Dec. 1995, pp. 1720–1722, https://umj.imath.kiev.ua/index.php/umj/article/view/5570.
Section
Short communications