2019
Том 71
№ 11

# Shevchik V. V.

Articles: 5
Brief Communications (English)

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

Ukr. Mat. Zh. - 1995. - 47, № 12. - pp. 1720–1722

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.

Brief Communications (Russian)

### Strict quasicomplements and the operators of dense imbedding

Ukr. Mat. Zh. - 1994. - 46, № 6. - pp. 789–792

A quasicomplement $М$ ofasubspace $N$ of a Banach space $X$ is called strict if $M$ does not contain an infinite-dimensional subspace $M_1$, such that the linear manifold $N + M_1$, is closed. It is proved that if $X$ is separable, then $N$ always has a strict quasicomplement. We study the properties of the dense imbedding operator restricted to infinite-dimensional closed subspaces of the space, where it is defined.

Article (Ukrainian)

### Action of an operator with nonclosed range on orthonormal bases in a Hilbert space

Ukr. Mat. Zh. - 1989. - 41, № 10. - pp. 1403–1407

Article (Ukrainian)

### Functional equations with shift in spaces of analytic functions in a halfplane

Ukr. Mat. Zh. - 1982. - 34, № 5. - pp. 661—666

Article (Ukrainian)

### The spectrum of a general singular operator

Ukr. Mat. Zh. - 1977. - 29, № 3. - pp. 423–426