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This article compares and analyzes Sufism and American personalist as two distinct intellectual traditions. Although they emerged in distinct historical and cultural contexts, but they conceptualized the human being as a holder of moral value, dignity, creative potential, spiritual embodiment. Tasavvuf expresses union with God and a spiritual journey to divine love, this path constitutes a profound ontological transformation of the Sufi practitioner. In the modern world a crisis of identity, cultural conflict, relativism in morality changed the value of humanity and for this reason the dialogue of sufy and personalist currents is a new highly valued philosophical approach. The coordination of the spiritual depth of Islamic-eastern philosophy and American-western ethics of responsibility as social issue opens new achievements in cultural dialogue and individual self-perfection. The synthesis of Sufism and American personalism creates a new model of “spiritual humanism”, here ethical and anthropological parallels are a new systematic analytical identification. Based on philosophical synthesis it formulates the idea of a “transcultural personalism embedded in spiritual responsibility”. The comparative philosophical ideas produce a spiritual-philosophical framework: from Sufism it adopts the ideas of love, mystical intuition, ontological unity, from Personalism it derives rational justification of responsibility, freedom, human dignity. Through this dialectical integration the human is accepted as a metaphysical reflection of the absolute essence and as an ethical-subjective actor in historical process. Both philosophical schools hold that the human being is responsible toward mankind and God. Sufism sees the implementation of these duties in spiritual perfection, in the same issue personalism realizes it by understanding the importance of social responsibility and ethical consciousness. As a final analysis, the sufi philosophy on “silent journey guiding the human existence toward the Divine” resonates with American personalism in its understanding of God`s manifestation with human being. Each philosophical study evaluates the human as a center of spiritual universe and claims that divine worth of person is the most significant philosophical truth. Overall, this approach provides a productive conceptual foundation not only for interreligious encounter, but also for the evolution of humanism in global philosophical thought. Emerging from the dialogue of Islamic mysticism and American-western personalism in the twenty first century the discussion offers a significant philosophical direction for reconsidering the concepts of the humanity, responsibility, spirituality.

In the Hilbert space ℓ 2 Ω (Z; E) (Z := {0,±1,±2, ...}, dim E = N < ∞), the maximal dissipative singular second-order matrix difference operators that the extensions of a minimal symmetric operator with maximal deficiency indices (2N, 2N) (in limit-circle cases at ±∞) are considered. The maximal dissipative operators with general boundary conditions are investigated. For the dissipative operator, a self-adjoint dilation and is its incoming and outgoing spectral representations are constructed. These constructions make it possible to determine the scattering matrix of the dilation. Also a functional model of the dissipative operator is constructed. Then its characteristic function in terms of the scattering matrix of the dilation is set. Finally, a theorem on the completeness of the system of root vectors of the dissipative operator is proved.