In this work, firstly in the Hilbert space of vector-functions all selfadjoint extensions of the minimal operator generated by linear singular symmetric differential expression with a selfadjoint operator coefficient in any Hilbert space are described in terms of boundary values. Later structure of the spectrum of these extensions is investigated.

In the present paper, we construct the minimal and maximal operators generated by special type linear differential-operator expression for first order in the weighted Hilbert space of vector-functions defined on right semi-axis with the use of standard technique. In this case, the minimal operator is accretive but not maximal. Our main goal in this paper is to describe the general form of all maximally accretive extensions of the minimal operator in the weighted Hilbert space of vector-functions. Using the Calkin-Gorbachuk method, the general representation of all maximally accretive extensions of this minimal operator in terms of boundary conditions is obtained. We also investigate the structure of the spectrum set such maximally accretive extensions of this type of minimal operator.

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