convert a list of vectors to data frame

df_list = lapply(a, function(x) data.frame(A = names(x), V = x, stringsAsFactors = FALSE))
dplyr::bind_rows(df_list, .id = "P")
#    P  A   V
# 1 p1 A1 1.0
# 2 p1 A2 0.5
# 3 p1 A3 0.3
# 4 p2 A3 2.0
# 5 p2 A4 2.5
# 6 p2 A5 2.3

I like the way above, but here's an option that might be more efficient on a large list:

data.frame(V = unlist(a)) %>% 
  tibble::rownames_to_column() %>%
  tidyr::separate(rowname, into = c("P", "A"))

One purrr and tibble option could be:

map_dfr(a, ~ enframe(., name = "A", value = "V"), .id = "P")

  P     A         V
  <chr> <chr> <dbl>
1 p1    A1      1  
2 p1    A2      0.5
3 p1    A3      0.3
4 p2    A3      2  
5 p2    A4      2.5
6 p2    A5      2.3

In base-R

cbind(stack(a),A=unlist(lapply(a,names),use.names = F))

gives

  values ind  A
1    1.0  p1 A1
2    0.5  p1 A2
3    0.3  p1 A3
4    2.0  p2 A3
5    2.5  p2 A4
6    2.3  p2 A5