The main result of the present paper by Markus and Matsaev can roughly be formulated as follows: Let \(L(x)\) be a smooth, operator valued function on \([0,1]\), selfadjoint and satisfying the following two conditions: \[ L(0)\ll 0, \quad L(1)\gg 1; \qquad (L(x)f,f)\delta \| f\|^ 2, \] for some positive constants \(\varepsilon\), \(\delta\) and any vector \(f\). Then there is a factorization \(L(x)=M(x)(Z-x)\) with \(M(x)\) a smooth and everywhere invertible operator- valued function and with \(Z\) similar to a selfadjoint operator with spectrum contained in the interval \([0,1]\). This result improves a recent similar result of the both authors. All previously known results along the same lines were proved for analytic functions in \(x\). The strength and novelty of the present approach consists in renouncing to the analyticity condition and by replacing it in the proofs with pseudoanalytic extensions of the function \(L\) to the complex plane.