M. V. Markin

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Articles: 6

On certain spectral features inherent to scalar type spectral operators

Marat V. Markin

↓ Abstract   |   Article (.pdf)

Methods Funct. Anal. Topology 23 (2017), no. 1, 60-65

Important spectral features such as the emptiness of the residual spectrum, countability of the point spectrum, provided the space is separable, and a characterization of spectral gap at 0, known to hold for bounded scalar type spectral operators, are shown to naturally transfer to the unbounded case.

On the generation of Beurling type Carleman ultradifferentiable $C_0$-semigroups by scalar type spectral operators

Marat V. Markin

↓ Abstract   |   Article (.pdf)

Methods Funct. Anal. Topology 22 (2016), no. 2, 169-183

A characterization of the scalar type spectral generators of Beurling type Carleman ultradifferentiable $C_0$-semigroups is established, the important case of the Gevrey ultradifferentiability is considered in detail, the implementation of the general criterion corresponding to a certain rapidly growing defining sequence is observed.

On the Carleman ultradifferentiable vectors of a scalar type spectral operator

Marat V. Markin

↓ Abstract   |   Article (.pdf)

Methods Funct. Anal. Topology 21 (2015), no. 4, 361-369

A description of the Carleman classes of vectors, in particular the Gevrey classes, of a scalar type spectral operator in a reflexive complex Banach space is shown to remain true without the reflexivity requirement. A similar nature description of the entire vectors of exponential type, known for a normal operator in a complex Hilbert space, is generalized to the case of a scalar type spectral operator in a complex Banach space.

A note on one decomposition of Banach spaces

M. V. Markin

↓ Abstract   |   Article (.pdf)

Methods Funct. Anal. Topology 12 (2006), no. 3, 254-257

For a scalar type spectral operator $A$ in complex Banach space $X$, the decomposition of $X$ into the direct sum \begin{equation*} X=\ker A\oplus \overline{R(A)}, \end{equation*} where $\ker A$ is the kernel of $A$ and $\overline{R(A)}$ is the closure of its range $R(A)$ is established.

A Gelfand-Mazur type theorem for normed algebras

Marat V. Markin

Methods Funct. Anal. Topology 11 (2005), no. 1, 63-64

On a characterization of the generators of analytic semigroups in the cass of normal operators

M. V. Markin

Methods Funct. Anal. Topology 2 (1996), no. 2, 86-93


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