The VSS is the negative side of the 15 volt supply. Single supply operation.

 

Your 1k resistors R1 and R4 do not split the 15V well enough.

A second opamp (use a dual 1458 for both) can be a follower with two 10k resistors biasing the +input at +7.5V then its +7.5V output can be a low impedance for the phantom ground.

 

Granted a dual op amp would be better. The design is to show that the circuit the TS was trying to achieve using a LM741 with a single supply is feasible. The 1K resistors are fine.

 

but you still cannot use, an LM358 for example, with a single power supply of +V and GND to invert a signal with a value below ground.

Yes, you can.

ak

 

Interesting that TI's LM358 has a common mode voltage that goes down to Vee, but On-Semi's LM358 has a common mode voltage that extends to -0.3V.
So, in theory, an inverting amplifier with the non-inverting input connected to ground should work.

No theory needed - been doing this since the 70's.

ak

 

Yes, the input voltage range includes ground on an LM358 or LM324 because they have PNP input transistors.