It is known that Kazhdan's (T) property is equivalent to the Serre's Property (FH), also known as the property of the fixed point of affine isoemmetric actions on a Hilbert space. The generalization of FH's properties to other Banach spaces seems to be poorly understood. During the lecture I will summarize the latest knowledge regarding this property. I will also explain the ideas of two statements. First is the fact that the Flp property implies Flq if 2 \neq q < p. Second is the fact that Property (T) implies FL_p ([0,1], \ mu) for every pw (1, \infty) if we limit our attention for actions that are measure-preserving.