Abstract. An asymmetric Fuglede-Putnam's Theorem for w -hyponormal operators and dominant operators is proved, as a consequence of this result, we obtain that the range of the generalized derivation induced by the above classes of operators is orthogonal to its kernel. Mathematics subject classification (2010): 47B47, 47A30, 47B20.

This article addresses the experimental characterization of the mechanical properties of three types of woven fabric composites taking into account the effects of hygrothermal and hygrothermomechanical aging. Characterization was carried out using the mode I, double cantilever beam (DCB) and the mode II, end notched flexural (ENF) interlaminar fracture tests in order to determine the loss in crack propagation resistance. The materials used were two types of woven (2/2 Twill, 8-Harness Satin) glass fiber, and 8-Harness Satin carbon fiber. The matrix was polyetherimide (PEI). The critical values of the energy release rate in mode I and mode II were calculated using the corrected beam theory. The material reinforced with 8-Harness Satin glass fiber presented the best behavior in mode I and mode II. The decrease in fracture strength is more important in the material reinforced with carbon fiber.

The present paper deals with the strain energy release rate of three woven fabric reinforced thermoplastic composites. The interlaminar fracture behavior was studied using the mode I, double cantilever beam test and the mode II, end notched flexure test, in order to determine the energy required for the initiation and growth of an artificial crack. The materials used were made of two types of glass fiber weave (2∕2 Twill, 8H Satin) and a carbon fiber (8H Satin). The matrix was polyetherimide. The delamination energy of these two materials was compared in order to study the effect of weave and reinforcement on mechanical properties. The fracture mechanism was also analyzed by means of scanning electron microscopy.

An asymmetric Fuglede-Putnam Theorem for certain posinormal operators is proved. As a consequence of this result, we obtain that the range of the generalized derivation induced by these classes of operators is orthogonal to its kernel. Mathematics Subject Classification: 47B47, 47A30, 47B20

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