2019
Том 71
№ 8

# Iokhvidov I. S.

Articles: 5
Article (Ukrainian)

### Asymptotics of certain sequences studied in the indefinite moments problem

Ukr. Mat. Zh. - 1983. - 35, № 6. - pp. 745–749

Article (Ukrainian)

### (r, k,l)-Characteristics of rectangular Toeplitz matrices

Ukr. Mat. Zh. - 1980. - 32, № 4. - pp. 477–482

Article (Ukrainian)

### Hankel and Toeplitz matrices and signatures of Toeplitz forms

Ukr. Mat. Zh. - 1967. - 19, № 1. - pp. 24–35

Article (Russian)

### On maximum definite lineals in a Hilbert space with a $G$ metric

Ukr. Mat. Zh. - 1965. - 17, № 4. - pp. 22-28

Article (Russian)

### On singular lineals in $\Pi_{\chi}$ spaces

Ukr. Mat. Zh. - 1964. - 16, № 3. - pp. 300-308

The author consider the Hilbert space $\mathfrak{H}$ in which a $J$-metric $[x, y] = (yx, y)$ is introduced, where $yj$ is the difference of two orthoprojections in $\mathfrak{H}$. The lineal $\mathfrak{L} \subset \mathfrak{H}$ is called definite if the form $[x, x] (x \in \mathfrak{L})$ has a constant sign; the lineal is called singular if the norms $(x, x)^{1/2}$ and $|[ x , x]|^{1/2}$ are nonequivalent. The properties of singular lineals are studied. In particular, it is shown that an arbitrary infinite-dimensional lineal with a positive Hermitian-bilinear metric $[x, y]$, complete with respact to the norm $|x| = [x, x]^{1/2}$ may, preserving the form $[x, y]$, be embeded into space $\Pi_{\chi}$ with an arbitary integer $\chi$ so that it proves to be a singular lineal with a given measure of singularity $m \leq \chi$.