Comparison of spectral invariants in Lagrangian and Hamiltonian Floer theory

Abstract: We compare spectral invariants in periodical orbits and Lagrangian Floer homology case, for closed symplectic manifold $P$ and its closed Lagrangian submanifolds $L$, when $\omega|{\pi_2(P,L)}=0$, and $\mu|{\pi_2(P,L)}=0$. From this result, we derive a corollary considering comparison of Hofer's distance in periodic orbits and Lagrangian case. We also define a product $HF_(H)\otimes HF_(L,\phi^1_H(L))\to HF_*(L,\phi^1_H(L))$ and prove subadditivity of invariants with respect to this product.