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Let $J$ and $R$ be anti-commuting fundamental symmetries in a Hilbert space$\mathfrak{H}$. The operators $J$ and $R$ can be interpreted as basis(generating) elements of the complex Clifford algebra ${\mathcalC}l_2(J,R):={span}\{I, J, R, iJR\}$. An arbitrary non-trivial fundamentalsymmetry from ${\mathcal C}l_2(J,R)$ is determined by the formula$J_{\vec{\alpha}}=\alpha_{1}J+\alpha_{2}R+\alpha_{3}iJR$, where${\vec{\alpha}}\in\mathbb{S}^2$.  Let $S$ be a symmetric operator that commutes with ${\mathcal C}l_2(J,R)$.The purpose of this paper is to study the sets $\Sigma_{{J_{\vec{\alpha}}}}$($\forall{\vec{\alpha}}\in\mathbb{S}^2$) of self-adjoint extensions of $S$ inKrein spaces generated by fundamental symmetries ${{J_{\vec{\alpha}}}}$(${{J_{\vec{\alpha}}}}$-self-adjoint extensions). We show that the sets$\Sigma_{{J_{\vec{\alpha}}}}$ and $\Sigma_{{J_{\vec{\beta}}}}$ are unitarilyequivalent for different ${\vec{\alpha}}, {\vec{\beta}}\in\mathbb{S}^2$ anddescribe in detail the structure of operators $A\in\Sigma_{{J_{\vec{\alpha}}}}$with empty resolvent set.

On self-adjoint operators in Krein spaces constructed by Clifford algebra Cl_2