‎in this article‎, ‎we have focused one some basic and productive information about the properties of spectrum and singular values related to compact operators which are ideals in a c*-algebra of bounded operators‎. ‎considering a two-sided connection between the family of symmetric gauge functions on sequence of singular values of compact operators and symmetric norms on finite dimensional operators‎, ‎then we express schatten p-ideals as an norm ideal‎, ‎in addition we study their properties‎. ‎note that since the space of bounded operators and the dual space of trace class operators are isomorphic‎, ‎we may define gel’fand integral for b(h)-valued functions‎. ‎having in mind and article name‎: ‎"d.‎ ‎r‎. ‎joci?‎, ‎cauchy–schwarz norm inequalities for weak*-integrals of operator valued functions"‎, ‎we concluded several version of cauchy–schwarz inequality for the b(h)-valued in the space of gel’fand integrable functions‎, ‎then we determined a generalization of these over norm ideals and schatten ideals‎. ‎at last accurate analization of the paper called:‎" ‎d‎. ‎r‎. ‎joci?‎, ‎d‎. ‎krtini?‎, ‎m‎. ‎s‎. ‎moslehian‎, ‎landau and grüss type inequalities for inner product type integral transformers in norm ideals"‎, ‎we prove a case of landau-grüss type inequalities for inner product type integral transformers structured whit b(h)-valued gel’fand integrable functions act on norm ideals.